Huang, Qiong-Ao; Zhang, Gengen; Wu, Bing Fully-discrete energy-preserving scheme for the space-fractional Klein-Gordon equation via Lagrange multiplier type scalar auxiliary variable approach. (English) Zbl 07431725 Math. Comput. Simul. 192, 265-277 (2022). MSC: 65-XX 81-XX PDF BibTeX XML Cite \textit{Q.-A. Huang} et al., Math. Comput. Simul. 192, 265--277 (2022; Zbl 07431725) Full Text: DOI OpenURL
Chou, Chih-Lung On the exact discretization of Schrödinger equation. (English) Zbl 1478.81012 Phys. Lett., A 386, Article ID 126986, 10 p. (2021). MSC: 81Q05 39A12 81S07 65T50 PDF BibTeX XML Cite \textit{C.-L. Chou}, Phys. Lett., A 386, Article ID 126986, 10 p. (2021; Zbl 1478.81012) Full Text: DOI arXiv OpenURL
Cuenin, Jean-Claude; Ikromov, Isroil A. Sharp time decay estimates for the discrete Klein-Gordon equation. (English) Zbl 1476.35133 Nonlinearity 34, No. 11, 7938-7962 (2021). MSC: 35L15 81Q05 39A12 35L05 PDF BibTeX XML Cite \textit{J.-C. Cuenin} and \textit{I. A. Ikromov}, Nonlinearity 34, No. 11, 7938--7962 (2021; Zbl 1476.35133) Full Text: DOI arXiv OpenURL
Li, Xueyang; Jiang, Kai Numerical simulation for quasiperiodic quantum dynamical systems. (Chinese. English summary) Zbl 07404348 J. Numer. Methods Comput. Appl. 42, No. 1, 3-17 (2021). MSC: 81-08 81Q05 65T50 PDF BibTeX XML Cite \textit{X. Li} and \textit{K. Jiang}, J. Numer. Methods Comput. Appl. 42, No. 1, 3--17 (2021; Zbl 07404348) Full Text: DOI OpenURL
Kholmatov, Shokhrukh Yu.; Lakaev, Saidakhmat N.; Almuratov, Firdavsjon M. Bound states of Schrödinger-type operators on one and two dimensional lattices. (English) Zbl 1467.81036 J. Math. Anal. Appl. 503, No. 1, Article ID 125280, 33 p. (2021). MSC: 81Q05 81Q35 47A10 60J20 82C41 35J10 PDF BibTeX XML Cite \textit{S. Yu. Kholmatov} et al., J. Math. Anal. Appl. 503, No. 1, Article ID 125280, 33 p. (2021; Zbl 1467.81036) Full Text: DOI arXiv OpenURL
Maeda, Masaya Stabilization of small solutions of discrete NLS with potential having two eigenvalues. (English) Zbl 1466.35330 Appl. Anal. 100, No. 8, 1603-1633 (2021). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35Q41 35B40 35C08 35B35 81Q05 PDF BibTeX XML Cite \textit{M. Maeda}, Appl. Anal. 100, No. 8, 1603--1633 (2021; Zbl 1466.35330) Full Text: DOI arXiv OpenURL
Maier, Daniela Breather solutions on discrete necklace graphs. (English) Zbl 1464.39015 Oper. Matrices 14, No. 3, 767-776 (2020). MSC: 39A36 39A12 39A28 35C08 PDF BibTeX XML Cite \textit{D. Maier}, Oper. Matrices 14, No. 3, 767--776 (2020; Zbl 1464.39015) Full Text: DOI OpenURL
Gradinaru, Vasile; Rietmann, Oliver A high-order integrator for the Schrödinger equation with time-dependent, homogeneous magnetic field. (English) Zbl 1462.81078 SMAI J. Comput. Math. 6, 253-271 (2020). MSC: 81Q05 35Q41 65M12 65M22 65T50 81V70 17B81 PDF BibTeX XML Cite \textit{V. Gradinaru} and \textit{O. Rietmann}, SMAI J. Comput. Math. 6, 253--271 (2020; Zbl 1462.81078) Full Text: DOI OpenURL
Pelinovsky, Dmitry E.; Penati, Tiziano; Paleari, Simone Existence and stability of Klein-Gordon breathers in the small-amplitude limit. (English) Zbl 1459.39046 Dörfler, Willy (ed.) et al., Mathematics of wave phenomena. Selected papers based on the presentations at the conference, Karlsruhe, Germany, July 23–27, 2018. Cham: Birkhäuser. Trends Math., 251-278 (2020). MSC: 39A36 39A14 39A12 37K60 37K40 PDF BibTeX XML Cite \textit{D. E. Pelinovsky} et al., in: Mathematics of wave phenomena. Selected papers based on the presentations at the conference, Karlsruhe, Germany, July 23--27, 2018. Cham: Birkhäuser. 251--278 (2020; Zbl 1459.39046) Full Text: DOI arXiv OpenURL
Muda, Yuslenita; Akbar, Fiki T.; Kusdiantara, Rudy; Gunara, Bobby E.; Susanto, Hadi Reduction of a damped, driven Klein-Gordon equation into a discrete nonlinear Schrödinger equation: justification and numerical comparison. (English) Zbl 1460.35330 Asymptotic Anal. 120, No. 1-2, 73-86 (2020). MSC: 35Q55 35Q51 35Q53 35C08 35A01 65L06 PDF BibTeX XML Cite \textit{Y. Muda} et al., Asymptotic Anal. 120, No. 1--2, 73--86 (2020; Zbl 1460.35330) Full Text: DOI arXiv OpenURL
Huang, Jianguo; Wu, Bo A new fast compact time integrator method for solving Klein-Gordon equations. (Chinese. English summary) Zbl 1463.65224 J. Nanjing Norm. Univ., Nat. Sci. Ed. 43, No. 2, 1-5 (2020). MSC: 65M06 65M99 65D05 65T50 65N06 PDF BibTeX XML Cite \textit{J. Huang} and \textit{B. Wu}, J. Nanjing Norm. Univ., Nat. Sci. Ed. 43, No. 2, 1--5 (2020; Zbl 1463.65224) Full Text: DOI OpenURL
Zhou, Kai; Yang, Jun; Ma, Liyuan; Shen, Shoufeng Symbolic computation of new exact solutions for some nonlinear equations in mathematical physics. (Chinese. English summary) Zbl 1463.68144 Appl. Math., Ser. A (Chin. Ed.) 35, No. 2, 223-234 (2020). MSC: 68W30 35C07 35C08 35Q51 35Q53 PDF BibTeX XML Cite \textit{K. Zhou} et al., Appl. Math., Ser. A (Chin. Ed.) 35, No. 2, 223--234 (2020; Zbl 1463.68144) Full Text: DOI OpenURL
Klopp, F.; Fedotov, A. A. On the hierarchical behavior of solutions of the Maryland equation in the semiclassical approximation. (English. Russian original) Zbl 1454.81067 Math. Notes 108, No. 6, 906-910 (2020); translation from Mat. Zametki 108, No. 6, 941-946 (2020). MSC: 81Q05 39A12 39A06 37C55 93A13 PDF BibTeX XML Cite \textit{F. Klopp} and \textit{A. A. Fedotov}, Math. Notes 108, No. 6, 906--910 (2020; Zbl 1454.81067); translation from Mat. Zametki 108, No. 6, 941--946 (2020) Full Text: DOI OpenURL
Molina, Mario I. The two-dimensional fractional discrete nonlinear Schrödinger equation. (English) Zbl 1448.34146 Phys. Lett., A 384, No. 33, Article ID 126835, 6 p. (2020). MSC: 34K37 35Q55 81Q05 PDF BibTeX XML Cite \textit{M. I. Molina}, Phys. Lett., A 384, No. 33, Article ID 126835, 6 p. (2020; Zbl 1448.34146) Full Text: DOI arXiv OpenURL
Hanif, Y.; Saleem, U. Degenerate and non-degenerate solutions of \(\mathcal{PT}\)-symmetric nonlocal integrable discrete nonlinear Schrödinger equation. (English) Zbl 1448.35471 Phys. Lett., A 384, No. 32, Article ID 126834, 11 p. (2020). MSC: 35Q55 39A12 81Q05 PDF BibTeX XML Cite \textit{Y. Hanif} and \textit{U. Saleem}, Phys. Lett., A 384, No. 32, Article ID 126834, 11 p. (2020; Zbl 1448.35471) Full Text: DOI OpenURL
Ji, Bingquan; Zhang, Luming Error estimates of a conservative finite difference Fourier pseudospectral method for the Klein-Gordon-Schrödinger equation. (English) Zbl 1453.65222 Comput. Math. Appl. 79, No. 7, 1956-1971 (2020). MSC: 65M06 65M70 65M15 35Q55 65T50 PDF BibTeX XML Cite \textit{B. Ji} and \textit{L. Zhang}, Comput. Math. Appl. 79, No. 7, 1956--1971 (2020; Zbl 1453.65222) Full Text: DOI OpenURL
Sushch, Volodymyr Chiral properties of discrete Joyce and Hestenes equations. (English) Zbl 1453.81019 Pinelas, Sandra (ed.) et al., Differential and difference equations with applications. Selected papers based on the presentations at the fourth international conference, ICDDEA 2019, Lisbon, Portugal, July 1–5, 2019. Cham: Springer. Springer Proc. Math. Stat. 333, 765-778 (2020). MSC: 81Q05 81R20 81R25 39A12 15A66 15A67 PDF BibTeX XML Cite \textit{V. Sushch}, Springer Proc. Math. Stat. 333, 765--778 (2020; Zbl 1453.81019) Full Text: DOI arXiv OpenURL
Wang, Jialing; Wang, Yushun An SDG Galerkin structure-preserving scheme for the Klein-Gordon-Schrödinger equation. (English) Zbl 1454.65121 Math. Methods Appl. Sci. 43, No. 9, 6011-6030 (2020). MSC: 65M60 65N30 65L05 65P10 65M12 35Q55 PDF BibTeX XML Cite \textit{J. Wang} and \textit{Y. Wang}, Math. Methods Appl. Sci. 43, No. 9, 6011--6030 (2020; Zbl 1454.65121) Full Text: DOI OpenURL
Martínez, Romeo; Macías-Díaz, J. E.; Hendy, A. S. Corrigendum to: “A numerically efficient and conservative model for a Riesz space-fractional Klein-Gordon-Zakharov system”. (English) Zbl 1470.65152 Commun. Nonlinear Sci. Numer. Simul. 83, Article ID 105109, 4 p. (2020). MSC: 65M06 35R11 35L53 35L70 PDF BibTeX XML Cite \textit{R. Martínez} et al., Commun. Nonlinear Sci. Numer. Simul. 83, Article ID 105109, 4 p. (2020; Zbl 1470.65152) Full Text: DOI OpenURL
Lin, Bin An efficient spline scheme of the coupled nonlinear Schrödinger equations. (English) Zbl 1448.81310 J. Math. Chem. 58, No. 8, 1663-1679 (2020). MSC: 81Q05 35Q55 81R05 35G50 37K06 39A12 65D07 PDF BibTeX XML Cite \textit{B. Lin}, J. Math. Chem. 58, No. 8, 1663--1679 (2020; Zbl 1448.81310) Full Text: DOI OpenURL
Sushch, Volodymyr A discrete version of plane wave solutions of the Dirac equation in the Joyce form. (English) Zbl 1447.39002 Adv. Appl. Clifford Algebr. 30, No. 3, Paper No. 46, 20 p. (2020). MSC: 39A12 81Q05 39A70 PDF BibTeX XML Cite \textit{V. Sushch}, Adv. Appl. Clifford Algebr. 30, No. 3, Paper No. 46, 20 p. (2020; Zbl 1447.39002) Full Text: DOI arXiv OpenURL
Zhang, Cheng; Peng, Linyu; Zhang, Da-jun Discrete Crum’s theorems and lattice KdV-type equations. (English. Russian original) Zbl 1445.81020 Theor. Math. Phys. 202, No. 2, 165-182 (2020); translation from Teor. Mat. Fiz. 202, No. 2, 187-206 (2020). MSC: 81Q05 39A12 39A05 37K35 35Q53 35Q55 35P05 35P30 PDF BibTeX XML Cite \textit{C. Zhang} et al., Theor. Math. Phys. 202, No. 2, 165--182 (2020; Zbl 1445.81020); translation from Teor. Mat. Fiz. 202, No. 2, 187--206 (2020) Full Text: DOI OpenURL
Suslov, Sergei K.; Vega-Guzmán, José M.; Barley, Kamal An introduction to special functions with some applications to quantum mechanics. (English) Zbl 1443.33026 Foupouagnigni, Mama (ed.) et al., Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5–12, 2018. Cham: Birkhäuser. Tutor. Sch. Workshops Math. Sci., 517-628 (2020). MSC: 33C45 81Q05 PDF BibTeX XML Cite \textit{S. K. Suslov} et al., in: Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5--12, 2018. Cham: Birkhäuser. 517--628 (2020; Zbl 1443.33026) Full Text: DOI OpenURL
Li, Meng; Huang, Chengming; Zhao, Yongliang Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation. (English) Zbl 1442.65168 Numer. Algorithms 84, No. 3, 1081-1119 (2020). MSC: 65M06 65N30 65M12 65F10 65F08 65T50 15B05 26A33 35R11 35Q55 PDF BibTeX XML Cite \textit{M. Li} et al., Numer. Algorithms 84, No. 3, 1081--1119 (2020; Zbl 1442.65168) Full Text: DOI OpenURL
Ji, Bingquan; Zhang, Luming A dissipative finite difference Fourier pseudo-spectral method for the Klein-Gordon-Schrödinger equations with damping mechanism. (English) Zbl 1474.65392 Appl. Math. Comput. 376, Article ID 125148, 16 p. (2020). MSC: 65M70 35L70 35Q55 65M12 74A50 PDF BibTeX XML Cite \textit{B. Ji} and \textit{L. Zhang}, Appl. Math. Comput. 376, Article ID 125148, 16 p. (2020; Zbl 1474.65392) Full Text: DOI OpenURL
Macías-Díaz, J. E. Existence of solutions of an explicit energy-conserving scheme for a fractional Klein-Gordon-Zakharov system. (English) Zbl 1433.65161 Appl. Numer. Math. 151, 40-43 (2020). MSC: 65M06 35R11 35Q53 35A01 PDF BibTeX XML Cite \textit{J. E. Macías-Díaz}, Appl. Numer. Math. 151, 40--43 (2020; Zbl 1433.65161) Full Text: DOI OpenURL
Maier, Daniela Construction of breather solutions for nonlinear Klein-Gordon equations on periodic metric graphs. (English) Zbl 1439.35336 J. Differ. Equations 268, No. 6, 2491-2509 (2020). MSC: 35L71 35L15 35R02 PDF BibTeX XML Cite \textit{D. Maier}, J. Differ. Equations 268, No. 6, 2491--2509 (2020; Zbl 1439.35336) Full Text: DOI arXiv OpenURL
Coskun, Nimet; Yokus, Nihal A note on the spectrum of discrete Klein-Gordon \(s\)-wave equation with eigenparameter dependent boundary condition. (English) Zbl 07534296 Filomat 33, No. 2, 449-455 (2019). MSC: 39A70 47A10 47A75 PDF BibTeX XML Cite \textit{N. Coskun} and \textit{N. Yokus}, Filomat 33, No. 2, 449--455 (2019; Zbl 07534296) Full Text: DOI OpenURL
Muda, Y.; Akbar, F. T.; Kusdiantara, R.; Gunara, B. E.; Susanto, H. Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons. (English) Zbl 1472.81083 Phys. Lett., A 383, No. 12, 1274-1282 (2019). MSC: 81Q05 35Q55 35P15 35A01 39A12 PDF BibTeX XML Cite \textit{Y. Muda} et al., Phys. Lett., A 383, No. 12, 1274--1282 (2019; Zbl 1472.81083) Full Text: DOI arXiv OpenURL
Likhachev, V. N.; Vinogradov, G. A. Solutions of the discrete nonlinear Schrödinger equation with a trap. (English. Russian original) Zbl 1441.81088 Theor. Math. Phys. 201, No. 3, 1771-1778 (2019); translation from Teor. Mat. Fiz. 201, No. 3, 415-423 (2019). MSC: 81Q05 35Q55 81Q15 39A12 41A58 PDF BibTeX XML Cite \textit{V. N. Likhachev} and \textit{G. A. Vinogradov}, Theor. Math. Phys. 201, No. 3, 1771--1778 (2019; Zbl 1441.81088); translation from Teor. Mat. Fiz. 201, No. 3, 415--423 (2019) Full Text: DOI OpenURL
Xiao, Aiguo; Wang, Junjie Symplectic scheme for the Schrödinger equation with fractional Laplacian. (English) Zbl 1423.81070 Appl. Numer. Math. 146, 469-487 (2019). MSC: 81Q05 34L40 34A08 39A12 53D05 34K28 PDF BibTeX XML Cite \textit{A. Xiao} and \textit{J. Wang}, Appl. Numer. Math. 146, 469--487 (2019; Zbl 1423.81070) Full Text: DOI OpenURL
Hong, Younghun; Yang, Changhun Uniform Strichartz estimates on the lattice. (English) Zbl 1433.35365 Discrete Contin. Dyn. Syst. 39, No. 6, 3239-3264 (2019). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35Q55 37K60 39A14 35Q53 35Q41 78A50 PDF BibTeX XML Cite \textit{Y. Hong} and \textit{C. Yang}, Discrete Contin. Dyn. Syst. 39, No. 6, 3239--3264 (2019; Zbl 1433.35365) Full Text: DOI arXiv OpenURL
Frantzeskakis, D. J.; Karachalios, N. I.; Kevrekidis, P. G.; Koukouloyannis, V.; Vetas, K. Dynamical transitions between equilibria in a dissipative Klein-Gordon lattice. (English) Zbl 1419.82011 J. Math. Anal. Appl. 472, No. 1, 546-576 (2019). Reviewer: Hasan Akin (Gaziantep) MSC: 82B20 35Q53 35B32 PDF BibTeX XML Cite \textit{D. J. Frantzeskakis} et al., J. Math. Anal. Appl. 472, No. 1, 546--576 (2019; Zbl 1419.82011) Full Text: DOI arXiv OpenURL
Wagner, Wolfgang A random walk model for the Schrödinger equation. (English) Zbl 1484.82048 Math. Comput. Simul. 143, 138-148 (2018). MSC: 82C41 35Q41 35Q55 60J20 60J25 60J74 81Q05 PDF BibTeX XML Cite \textit{W. Wagner}, Math. Comput. Simul. 143, 138--148 (2018; Zbl 1484.82048) Full Text: DOI OpenURL
Bayindir, Cihan Compressive spectral renormalization method. (English) Zbl 1414.81084 TWMS J. Appl. Eng. Math. 8, No. 2, 425-437 (2018). MSC: 81Q05 65T50 PDF BibTeX XML Cite \textit{C. Bayindir}, TWMS J. Appl. Eng. Math. 8, No. 2, 425--437 (2018; Zbl 1414.81084) Full Text: arXiv OpenURL
Sushch, Volodymyr Discrete versions of some Dirac type equations and plane wave solutions. (English) Zbl 1407.81096 Pinelas, Sandra (ed.) et al., Differential and difference equations with applications. ICDDEA, Amadora, Portugal, June 5–9, 2017. Cham: Springer. Springer Proc. Math. Stat. 230, 463-475 (2018). MSC: 81Q05 39A12 39A70 PDF BibTeX XML Cite \textit{V. Sushch}, Springer Proc. Math. Stat. 230, 463--475 (2018; Zbl 1407.81096) Full Text: DOI arXiv OpenURL
Sushch, Volodymyr A discrete Dirac-Kähler equation using a geometric discretisation scheme. (English) Zbl 1403.39007 Adv. Appl. Clifford Algebr. 28, No. 4, Paper No. 72, 17 p. (2018). Reviewer: Alex B. Gaina (Chisinau) MSC: 39A12 81Q05 39A70 PDF BibTeX XML Cite \textit{V. Sushch}, Adv. Appl. Clifford Algebr. 28, No. 4, Paper No. 72, 17 p. (2018; Zbl 1403.39007) Full Text: DOI arXiv OpenURL
Laliena, Victor; Campo, Javier An improved discretization of Schrödinger-like radial equations. (English) Zbl 1397.81063 J. Phys. A, Math. Theor. 51, No. 32, Article ID 325203, 14 p. (2018). MSC: 81Q05 81Q10 81R05 34L40 65L12 39A12 PDF BibTeX XML Cite \textit{V. Laliena} and \textit{J. Campo}, J. Phys. A, Math. Theor. 51, No. 32, Article ID 325203, 14 p. (2018; Zbl 1397.81063) Full Text: DOI arXiv OpenURL
Koornwinder, Tom; Kostenko, Aleksey; Teschl, Gerald Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. (English) Zbl 1405.33012 Adv. Math. 333, 796-821 (2018). Reviewer: Nicolae Cotfas (Bucureşti) MSC: 33C45 47B36 81U30 81Q05 PDF BibTeX XML Cite \textit{T. Koornwinder} et al., Adv. Math. 333, 796--821 (2018; Zbl 1405.33012) Full Text: DOI arXiv OpenURL
Wang, Jialing; Wang, Yushun; Liang, Dong Analysis of a Fourier pseudo-spectral conservative scheme for the Klein-Gordon-Schrödinger equation. (English) Zbl 1390.65082 Int. J. Comput. Math. 95, No. 1, 36-60 (2018). MSC: 65M06 65M12 65M20 65M70 65T50 PDF BibTeX XML Cite \textit{J. Wang} et al., Int. J. Comput. Math. 95, No. 1, 36--60 (2018; Zbl 1390.65082) Full Text: DOI OpenURL
Borrelli, William Multiple solutions for a self-consistent Dirac equation in two dimensions. (English) Zbl 1393.81013 J. Math. Phys. 59, No. 4, 041503, 13 p. (2018). Reviewer: Piotr Garbaczewski (Opole) MSC: 81Q10 82C70 82D80 35Q55 35L86 81Q05 46E39 47A10 47B06 35S15 PDF BibTeX XML Cite \textit{W. Borrelli}, J. Math. Phys. 59, No. 4, 041503, 13 p. (2018; Zbl 1393.81013) Full Text: DOI arXiv OpenURL
Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya; Sakhnovich, A. L. Continuous and discrete dynamical Schrödinger systems: explicit solutions. (English) Zbl 1387.81207 J. Phys. A, Math. Theor. 51, No. 1, Article ID 015202, 15 p. (2018). MSC: 81Q05 39A12 81U15 37K35 PDF BibTeX XML Cite \textit{B. Fritzsche} et al., J. Phys. A, Math. Theor. 51, No. 1, Article ID 015202, 15 p. (2018; Zbl 1387.81207) Full Text: DOI arXiv OpenURL
Bayindir, C. Rogue wavefunctions due to noisy quantum tunneling potentials. (English) Zbl 1388.81100 TWMS J. Appl. Eng. Math. 7, No. 2, 236-247 (2017). MSC: 81Q05 65T50 35Q55 35P30 60H40 35C08 81Q50 92D20 PDF BibTeX XML Cite \textit{C. Bayindir}, TWMS J. Appl. Eng. Math. 7, No. 2, 236--247 (2017; Zbl 1388.81100) Full Text: arXiv OpenURL
Melezhik, Vladimir S.; Sevastianov, Leonid A. Quantum-semiclassical calculation of transition probabilities in antiproton collisions with helium ions. (English) Zbl 1385.81046 Rykov, Vladimir V. (ed.) et al., Analytical and computational methods in probability theory. First international conference, ACMPT 2017, Moscow, Russia, October 23–27, 2017. Proceedings. Cham: Springer (ISBN 978-3-319-71503-2/pbk; 978-3-319-71504-9/ebook). Lecture Notes in Computer Science 10684, 449-460 (2017). MSC: 81U35 81V35 81Q05 81Q20 39A12 81V45 PDF BibTeX XML Cite \textit{V. S. Melezhik} and \textit{L. A. Sevastianov}, Lect. Notes Comput. Sci. 10684, 449--460 (2017; Zbl 1385.81046) Full Text: DOI OpenURL
Cuevas-Maraver, J.; Kevrekidis, P. G.; Aceves, A. B.; Saxena, Avadh Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum. (English) Zbl 1380.81103 J. Phys. A, Math. Theor. 50, No. 49, Article ID 495207, 17 p. (2017). MSC: 81Q05 81R20 35C08 35Q55 35Q51 PDF BibTeX XML Cite \textit{J. Cuevas-Maraver} et al., J. Phys. A, Math. Theor. 50, No. 49, Article ID 495207, 17 p. (2017; Zbl 1380.81103) Full Text: DOI arXiv Link OpenURL
Schmidt, Burkhard; Lorenz, Ulf WavePacket: a Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations. (English) Zbl 1376.81005 Comput. Phys. Commun. 213, 223-234 (2017). MSC: 81-04 65Y15 35Q41 81Q05 PDF BibTeX XML Cite \textit{B. Schmidt} and \textit{U. Lorenz}, Comput. Phys. Commun. 213, 223--234 (2017; Zbl 1376.81005) Full Text: DOI arXiv OpenURL
Weinmüller, Markus; Weinmüller, Michael; Rohland, Jonathan; Scrinzi, Armin Perfect absorption in Schrödinger-like problems using non-equidistant complex grids. (English) Zbl 1380.65189 J. Comput. Phys. 333, 199-211 (2017). MSC: 65M06 65M60 81Q05 PDF BibTeX XML Cite \textit{M. Weinmüller} et al., J. Comput. Phys. 333, 199--211 (2017; Zbl 1380.65189) Full Text: DOI arXiv OpenURL
Morfonios, Christian V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P. Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays. (English) Zbl 1372.82025 Ann. Phys. 385, 623-649 (2017). MSC: 82C10 82C20 39A12 81Q05 81Q37 PDF BibTeX XML Cite \textit{C. V. Morfonios} et al., Ann. Phys. 385, 623--649 (2017; Zbl 1372.82025) Full Text: DOI arXiv OpenURL
Krämer, Patrick; Schratz, Katharina Efficient time integration of the Maxwell-Klein-Gordon equation in the non-relativistic limit regime. (English) Zbl 1375.78015 J. Comput. Appl. Math. 316, 247-259 (2017). MSC: 78A35 81T13 35C20 78M35 78M22 65T50 35Q60 78M30 35B45 PDF BibTeX XML Cite \textit{P. Krämer} and \textit{K. Schratz}, J. Comput. Appl. Math. 316, 247--259 (2017; Zbl 1375.78015) Full Text: DOI OpenURL
Caliari, M.; Ostermann, A.; Piazzola, C. A splitting approach for the magnetic Schrödinger equation. (English) Zbl 1373.81195 J. Comput. Appl. Math. 316, 74-85 (2017). MSC: 81Q05 78A25 42B05 42B10 65T50 81T80 PDF BibTeX XML Cite \textit{M. Caliari} et al., J. Comput. Appl. Math. 316, 74--85 (2017; Zbl 1373.81195) Full Text: DOI arXiv OpenURL
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime. (English) Zbl 1370.81053 J. Sci. Comput. 71, No. 3, 1094-1134 (2017). MSC: 81Q05 65M06 39A12 65T50 94B65 81-08 PDF BibTeX XML Cite \textit{W. Bao} et al., J. Sci. Comput. 71, No. 3, 1094--1134 (2017; Zbl 1370.81053) Full Text: DOI arXiv OpenURL
Borovyk, Vita; Goldberg, Michael The Klein-Gordon equation on \(\mathbb Z^2\) and the quantum harmonic lattice. (English. French summary) Zbl 1378.35182 J. Math. Pures Appl. (9) 107, No. 6, 667-696 (2017). MSC: 35L15 35L05 81Q05 42B20 81Q35 PDF BibTeX XML Cite \textit{V. Borovyk} and \textit{M. Goldberg}, J. Math. Pures Appl. (9) 107, No. 6, 667--696 (2017; Zbl 1378.35182) Full Text: DOI arXiv OpenURL
Chen, Hu; Lü, Shujuan; Chen, Wenping A fully discrete spectral method for the nonlinear time fractional Klein-Gordon equation. (English) Zbl 1357.35281 Taiwanese J. Math. 21, No. 1, 231-251 (2017). MSC: 35R11 35Q53 PDF BibTeX XML Cite \textit{H. Chen} et al., Taiwanese J. Math. 21, No. 1, 231--251 (2017; Zbl 1357.35281) Full Text: DOI OpenURL
Tarasov, Vasily E. Exact discretization of Schrödinger equation. (English) Zbl 1377.39010 Phys. Lett., A 380, No. 1-2, 68-75 (2016). MSC: 39A12 81Q05 PDF BibTeX XML Cite \textit{V. E. Tarasov}, Phys. Lett., A 380, No. 1--2, 68--75 (2016; Zbl 1377.39010) Full Text: DOI OpenURL
Sushch, Volodymyr Discrete Dirac-Kähler equation and its formulation in algebraic form. (English) Zbl 1389.39032 PLISKA, Stud. Math. 26, 225-238 (2016). Reviewer: Angela Slavova (Sofia) MSC: 39A60 39A12 39A70 81Q05 PDF BibTeX XML Cite \textit{V. Sushch}, PLISKA, Stud. Math. 26, 225--238 (2016; Zbl 1389.39032) Full Text: arXiv Link OpenURL
Judge, Edmund; Naboko, Sergey; Wood, Ian Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach. (English) Zbl 1360.81145 Integral Equations Oper. Theory 85, No. 3, 427-450 (2016). MSC: 81Q05 39A12 35J10 35P05 81Q10 PDF BibTeX XML Cite \textit{E. Judge} et al., Integral Equations Oper. Theory 85, No. 3, 427--450 (2016; Zbl 1360.81145) Full Text: DOI arXiv Link OpenURL
Sushch, Volodymyr Discrete Dirac-Kähler and Hestenes equations. (English) Zbl 1355.81078 Pinelas, Sandra (ed.) et al., Differential and difference equations with applications. ICDDEA, Amadora, Portugal, May 18–22, 2015. Selected contributions. Cham: Springer (ISBN 978-3-319-32855-3/hbk; 978-3-319-32857-7/ebook). Springer Proceedings in Mathematics & Statistics 164, 433-442 (2016). MSC: 81Q05 39A12 81R05 PDF BibTeX XML Cite \textit{V. Sushch}, Springer Proc. Math. Stat. 164, 433--442 (2016; Zbl 1355.81078) Full Text: DOI arXiv OpenURL
El-Nabulsi, Rami Ahmad On nonlocal complexified Schrödinger equation and emergence of discrete quantum mechanics. (English) Zbl 1352.81027 Quantum Stud. Math. Found. 3, No. 4, 327-335 (2016). MSC: 81Q05 81P05 PDF BibTeX XML Cite \textit{R. A. El-Nabulsi}, Quantum Stud. Math. Found. 3, No. 4, 327--335 (2016; Zbl 1352.81027) Full Text: DOI OpenURL
Zhang, Yufeng; Rui, Wenjuan A few continuous and discrete dynamical systems. (English) Zbl 1351.37254 Rep. Math. Phys. 78, No. 1, 19-32 (2016). MSC: 37K10 81Q05 17B80 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{W. Rui}, Rep. Math. Phys. 78, No. 1, 19--32 (2016; Zbl 1351.37254) Full Text: DOI OpenURL
Cuccagna, Scipio; Maeda, Masaya; Phan, Tuoc V. On small energy stabilization in the NLKG with a trapping potential. (English) Zbl 1356.35142 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 146, 32-58 (2016). Reviewer: Michael Reissig (Freiberg) MSC: 35L71 35L15 PDF BibTeX XML Cite \textit{S. Cuccagna} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 146, 32--58 (2016; Zbl 1356.35142) Full Text: DOI arXiv OpenURL
Smirnov, A. B.; Fedotov, A. A. Adiabatic evolution generated by a Schrödinger operator with discrete and continuous spectra. (English. Russian original) Zbl 1342.35084 Funct. Anal. Appl. 50, No. 1, 76-79 (2016); translation from Funkts. Anal. Prilozh. 50, No. 1, 90-93 (2016). MSC: 35J10 81Q05 PDF BibTeX XML Cite \textit{A. B. Smirnov} and \textit{A. A. Fedotov}, Funct. Anal. Appl. 50, No. 1, 76--79 (2016; Zbl 1342.35084); translation from Funkts. Anal. Prilozh. 50, No. 1, 90--93 (2016) Full Text: DOI OpenURL
Èshkabilov, Yu. Kh. Spectrum of a model three-particle Schrödinger operator. (English. Russian original) Zbl 1338.81198 Theor. Math. Phys. 186, No. 2, 268-279 (2016); translation from Teor. Mat. Fiz. 186, No. 2, 311-322 (2016). MSC: 81Q10 81Q05 35J10 35P05 PDF BibTeX XML Cite \textit{Yu. Kh. Èshkabilov}, Theor. Math. Phys. 186, No. 2, 268--279 (2016; Zbl 1338.81198); translation from Teor. Mat. Fiz. 186, No. 2, 311--322 (2016) Full Text: DOI OpenURL
Muminov, M. E.; Shermatova, Yo. M. On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice. (English. Russian original) Zbl 1336.81036 Russ. Math. 60, No. 1, 22-29 (2016); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 1, 27-35 (2016). MSC: 81Q10 81Q05 81Q35 81V17 82D25 PDF BibTeX XML Cite \textit{M. E. Muminov} and \textit{Yo. M. Shermatova}, Russ. Math. 60, No. 1, 22--29 (2016; Zbl 1336.81036); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 1, 27--35 (2016) Full Text: DOI OpenURL
Kauffman, Louis H. Iterants, fermions and Majorana operators. (English) Zbl 1334.81035 Amoroso, Richard L. (ed.) et al., Unified field mechanics: natural science beyond the veil of spacetime. Proceedings of the IX symposium honoring noted French mathematical physicist Jean-Pierre Vigier, Morgan State University, Baltimore, MD, USA, November 16–19, 2014. Hackensack, NJ: World Scientific (ISBN 978-981-4719-05-6/hbk; 978-981-4719-07-0/ebook). 1-32 (2016). MSC: 81Q05 81R20 81R25 39A12 PDF BibTeX XML Cite \textit{L. H. Kauffman}, in: Unified field mechanics: natural science beyond the veil of spacetime. Proceedings of the IX symposium honoring noted French mathematical physicist Jean-Pierre Vigier, Morgan State University, Baltimore, MD, USA, November 16--19, 2014. Hackensack, NJ: World Scientific. 1--32 (2016; Zbl 1334.81035) Full Text: DOI OpenURL
Raikov, Georgi Discrete spectrum for Schrödinger operators with oscillating decaying potentials. (English) Zbl 1333.81142 J. Math. Anal. Appl. 438, No. 2, 551-564 (2016). MSC: 81Q05 81Q10 35J10 35P05 PDF BibTeX XML Cite \textit{G. Raikov}, J. Math. Anal. Appl. 438, No. 2, 551--564 (2016; Zbl 1333.81142) Full Text: DOI arXiv OpenURL
Faustino, Nelson Solutions for the Klein-Gordon and Dirac equations on the lattice based on Chebyshev polynomials. (English) Zbl 1332.30077 Complex Anal. Oper. Theory 10, No. 2, 379-399 (2016). MSC: 30G35 39A12 PDF BibTeX XML Cite \textit{N. Faustino}, Complex Anal. Oper. Theory 10, No. 2, 379--399 (2016; Zbl 1332.30077) Full Text: DOI arXiv OpenURL
Kopylova, Elena; Teschl, Gerald Dispersion estimates for one-dimensional discrete Dirac equations. (English) Zbl 1330.35366 J. Math. Anal. Appl. 434, No. 1, 191-208 (2016). MSC: 35Q41 35P25 81Q05 PDF BibTeX XML Cite \textit{E. Kopylova} and \textit{G. Teschl}, J. Math. Anal. Appl. 434, No. 1, 191--208 (2016; Zbl 1330.35366) Full Text: DOI arXiv OpenURL
Cervenka, Johann; Ellinghaus, Paul; Nedjalkov, Mihail Deterministic solution of the discrete Wigner equation. (English) Zbl 1361.81085 Dimov, Ivan (ed.) et al., Numerical methods and applications. 8th international conference, NMA 2014, Borovets, Bulgaria, August 20–24, 2014. Revised selected papers. Berlin: Springer (ISBN 978-3-319-15584-5/pbk). Lecture Notes in Computer Science 8962, 149-156 (2015). MSC: 81S30 81Q05 39A12 81T80 PDF BibTeX XML Cite \textit{J. Cervenka} et al., Lect. Notes Comput. Sci. 8962, 149--156 (2015; Zbl 1361.81085) Full Text: DOI OpenURL
Sushch, Volodymyr On the chirality of a discrete Dirac-Kähler equation. (English) Zbl 1334.81042 Rep. Math. Phys. 76, No. 2, 179-196 (2015). MSC: 81Q05 39A12 81R05 PDF BibTeX XML Cite \textit{V. Sushch}, Rep. Math. Phys. 76, No. 2, 179--196 (2015; Zbl 1334.81042) Full Text: DOI arXiv OpenURL
Aktosun, Tuncay; Papanicolaou, Vassilis G. Inverse problem with transmission eigenvalues for the discrete Schrödinger equation. (English) Zbl 1323.81024 J. Math. Phys. 56, No. 8, 082101, 36 p. (2015). Reviewer: Mohammad Sal Moslehian (Karlstad) MSC: 81Q05 39A12 81U40 PDF BibTeX XML Cite \textit{T. Aktosun} and \textit{V. G. Papanicolaou}, J. Math. Phys. 56, No. 8, 082101, 36 p. (2015; Zbl 1323.81024) Full Text: DOI arXiv OpenURL
Odake, Satoru; Sasaki, Ryu Solvable discrete quantum mechanics: \(q\)-orthogonal polynomials with \(\left|q\right| = 1\) and quantum dilogarithm. (English) Zbl 1326.81091 J. Math. Phys. 56, No. 7, 073502, 25 p. (2015). Reviewer: Giovanni Rastelli (Vercelli) MSC: 81Q80 81Q05 39A12 PDF BibTeX XML Cite \textit{S. Odake} and \textit{R. Sasaki}, J. Math. Phys. 56, No. 7, 073502, 25 p. (2015; Zbl 1326.81091) Full Text: DOI arXiv OpenURL
Bradji, Abdallah A theoretical analysis for a new finite volume scheme for a linear Schrödinger evolution equation on general nonconforming spatial meshes. (English) Zbl 1335.65076 Numer. Funct. Anal. Optim. 36, No. 5, 590-623 (2015). Reviewer: Przemysław Stpiczyński (Lublin) MSC: 65M08 35Q41 65M12 81Q05 81-08 65M50 PDF BibTeX XML Cite \textit{A. Bradji}, Numer. Funct. Anal. Optim. 36, No. 5, 590--623 (2015; Zbl 1335.65076) Full Text: DOI OpenURL
Huang, Meihua; Zhou, Zhan Ground state solutions of the periodic discrete coupled nonlinear Schrödinger equations. (English) Zbl 1325.39003 Math. Methods Appl. Sci. 38, No. 8, 1682-1695 (2015). Reviewer: Miloš Čanak (Beograd) MSC: 39A12 35Q55 81Q05 39A14 PDF BibTeX XML Cite \textit{M. Huang} and \textit{Z. Zhou}, Math. Methods Appl. Sci. 38, No. 8, 1682--1695 (2015; Zbl 1325.39003) Full Text: DOI OpenURL
Majumdar, Debasish Dark matter. An introduction. (English) Zbl 1305.81004 Boca Raton, FL: CRC Press (ISBN 978-1-4665-7211-9/hbk; 978-1-4665-7212-6/ebook). xi, 257 p. (2015). Reviewer: Claudia-Veronika Meister (Darmstadt) MSC: 81-02 83-02 81V22 83F05 85A40 00A79 PDF BibTeX XML Cite \textit{D. Majumdar}, Dark matter. An introduction. Boca Raton, FL: CRC Press (2015; Zbl 1305.81004) Full Text: DOI OpenURL
Mennemann, Jan-Frederik; Jüngel, Ansgar Perfectly matched layers versus discrete transparent boundary conditions in quantum device simulations. (English) Zbl 1349.81033 J. Comput. Phys. 275, 1-24 (2014). MSC: 81P15 81Q05 PDF BibTeX XML Cite \textit{J.-F. Mennemann} and \textit{A. Jüngel}, J. Comput. Phys. 275, 1--24 (2014; Zbl 1349.81033) Full Text: DOI arXiv OpenURL
Wen, Xiao-Yong; Wang, Deng-Shan Odd-soliton solutions and inelastic interaction for the differential-difference nonlinear Schrödinger equation in nonlinear optics. (English) Zbl 1335.81071 Appl. Math. Comput. 244, 598-605 (2014). MSC: 81Q05 39A12 35Q55 PDF BibTeX XML Cite \textit{X.-Y. Wen} and \textit{D.-S. Wang}, Appl. Math. Comput. 244, 598--605 (2014; Zbl 1335.81071) Full Text: DOI OpenURL
Makarov, V. L.; Dragunov, D. V.; Sember, D. A. Conditions of convergence and algorithmic aspects of program implementation of FD-method of solution the Cauchy problem for nonlinear Klein-Gordon equation. (Ukrainian. English summary) Zbl 1340.65173 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 198-238 (2014). MSC: 65M06 35Q40 65M12 PDF BibTeX XML Cite \textit{V. L. Makarov} et al., Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 198--238 (2014; Zbl 1340.65173) OpenURL
Makarov, V. L.; Dragunov, D. V.; Sember, D. A. A functional discrete method (FD-method) for solving the Cauchy problem for a nonlinear Klein-Gordon equation. (Ukrainian. English summary) Zbl 1313.65243 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2014, No. 10, 33-39 (2014). MSC: 65M12 35Q40 65M06 PDF BibTeX XML Cite \textit{V. L. Makarov} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2014, No. 10, 33--39 (2014; Zbl 1313.65243) Full Text: DOI OpenURL
D’Ambroise, J.; Lepri, S.; Malomed, B. A.; Kevrekidis, P. G. \(\mathcal{PT}\)-symmetric ladders with a scattering core. (English) Zbl 1298.35192 Phys. Lett., A 378, No. 38-39, 2824-2830 (2014). MSC: 35Q55 35B35 81Q05 PDF BibTeX XML Cite \textit{J. D'Ambroise} et al., Phys. Lett., A 378, No. 38--39, 2824--2830 (2014; Zbl 1298.35192) Full Text: DOI arXiv OpenURL
Makarov, V. L.; Drahunov, D. V.; Sember, D. S. Algorithmic aspects of software realization of the FD-method for the solution of the nonlinear Klein-Gordon equation. (English. Ukrainian original) Zbl 1300.65059 J. Math. Sci., New York 197, No. 1, 77-91 (2014); translation from Neliniĭni Kolyvannya 16, No. 1, 75-89 (2013). MSC: 65M06 35Q40 65Y20 PDF BibTeX XML Cite \textit{V. L. Makarov} et al., J. Math. Sci., New York 197, No. 1, 77--91 (2014; Zbl 1300.65059); translation from Neliniĭni Kolyvannya 16, No. 1, 75--89 (2013) Full Text: DOI OpenURL
Sushch, Volodymyr A discrete model of the Dirac-Kähler equation. (English) Zbl 1288.81037 Rep. Math. Phys. 73, No. 1, 109-125 (2014). MSC: 81Q05 39A12 PDF BibTeX XML Cite \textit{V. Sushch}, Rep. Math. Phys. 73, No. 1, 109--125 (2014; Zbl 1288.81037) Full Text: DOI arXiv OpenURL
Temirgaliyev, N.; Sherniyazov, K. Y.; Berikkhanova, M. Y. Exact orders of computational (numerical) diameters in problems of reconstructing functions and sampling solutions of the Klein-Gordon equation from Fourier coefficients. (English. Russian original) Zbl 1308.35254 Proc. Steklov Inst. Math. 282, Suppl. 1, S165-S191 (2013); translation from Sovrem. Probl. Mat. 17, 179-207 (2013). MSC: 35Q53 65T50 PDF BibTeX XML Cite \textit{N. Temirgaliyev} et al., Proc. Steklov Inst. Math. 282, S165--S191 (2013; Zbl 1308.35254); translation from Sovrem. Probl. Mat. 17, 179--207 (2013) Full Text: DOI OpenURL
James, Guillaume; Kevrekidis, Panayotis G.; Cuevas, Jesús Breathers in oscillator chains with Hertzian interactions. (English) Zbl 1278.37053 Physica D 251, 39-59 (2013). MSC: 37K60 35B05 81Q05 PDF BibTeX XML Cite \textit{G. James} et al., Physica D 251, 39--59 (2013; Zbl 1278.37053) Full Text: DOI arXiv OpenURL
Tinyukova, T. S. Scattering in the case of the discrete Schrödinger operator for intersected quantum wires. (Russian. English summary) Zbl 1299.81022 Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki 2012, No. 3, 74-84 (2012). MSC: 81Q05 81U05 PDF BibTeX XML Cite \textit{T. S. Tinyukova}, Vestn. Udmurt. Univ., Mat. Mekh. Komp'yut. Nauki 2012, No. 3, 74--84 (2012; Zbl 1299.81022) Full Text: DOI MNR OpenURL
Bourgain, Jean Moebius Schrödinger. (English) Zbl 1319.35135 Klartag, Bo’az (ed.) et al., Geometric aspects of functional analysis. Proceedings of the Israel seminar (GAFA) 2006–2010. Berlin: Springer (ISBN 978-3-642-29848-6/pbk; 978-3-642-29849-3/ebook). Lecture Notes in Mathematics 2050, 143-150 (2012). Reviewer: Roger A. Nichols (Chattanooga) MSC: 35P20 35P15 39A12 39A70 81Q05 82B44 35J10 PDF BibTeX XML Cite \textit{J. Bourgain}, Lect. Notes Math. 2050, 143--150 (2012; Zbl 1319.35135) Full Text: DOI arXiv OpenURL
Tawfik, Sherif A. Localized states in an ultracold atomic gas trapped in a bichromatic potential: the effect of a time-varying phase. (English) Zbl 1253.81057 Commun. Nonlinear Sci. Numer. Simul. 17, No. 9, 3552-3557 (2012). MSC: 81Q05 82D05 82B44 35Q55 39A12 78A37 PDF BibTeX XML Cite \textit{S. A. Tawfik}, Commun. Nonlinear Sci. Numer. Simul. 17, No. 9, 3552--3557 (2012; Zbl 1253.81057) Full Text: DOI OpenURL
Szalay, Viktor; Szidarovszky, Tamás; Czakó, Gábor; Császár, Attila G. A paradox of grid-based representation techniques: accurate eigenvalues from inaccurate matrix elements. (English) Zbl 1251.81039 J. Math. Chem. 50, No. 3, 636-651 (2012). MSC: 81Q05 81V55 39A12 81T80 PDF BibTeX XML Cite \textit{V. Szalay} et al., J. Math. Chem. 50, No. 3, 636--651 (2012; Zbl 1251.81039) Full Text: DOI OpenURL
James, Guillaume; Pelinovsky, Dmitry Breather continuation from infinity in nonlinear oscillator chains. (English) Zbl 1283.37069 Discrete Contin. Dyn. Syst. 32, No. 5, 1775-1799 (2012). Reviewer: Dimitar A. Kolev (Sofia) MSC: 37K50 37K60 37N25 PDF BibTeX XML Cite \textit{G. James} and \textit{D. Pelinovsky}, Discrete Contin. Dyn. Syst. 32, No. 5, 1775--1799 (2012; Zbl 1283.37069) Full Text: DOI arXiv OpenURL
Znojil, Miloslav \(N\)-site-lattice analogues of \(V(x) = \text ix^3\). (English) Zbl 1243.81076 Ann. Phys. 327, No. 3, 893-913 (2012). MSC: 81Q05 81Q12 39A12 PDF BibTeX XML Cite \textit{M. Znojil}, Ann. Phys. 327, No. 3, 893--913 (2012; Zbl 1243.81076) Full Text: DOI arXiv OpenURL
Chatterjee, Sourav; Kirkpatrick, Kay Probabilistic methods for discrete nonlinear Schrödinger equations. (English) Zbl 1273.35249 Commun. Pure Appl. Math. 65, No. 5, 727-757 (2012). Reviewer: Isamu Dôku (Saitama) MSC: 35Q55 60H30 81Q05 PDF BibTeX XML Cite \textit{S. Chatterjee} and \textit{K. Kirkpatrick}, Commun. Pure Appl. Math. 65, No. 5, 727--757 (2012; Zbl 1273.35249) Full Text: DOI arXiv OpenURL
Bauke, Heiko; Keitel, Christoph H. Accelerating the Fourier split operator method via graphics processing units. (English) Zbl 1261.65101 Comput. Phys. Commun. 182, No. 12, 2454-2463 (2011). MSC: 65M70 35Q55 35Q40 81Q05 65T50 PDF BibTeX XML Cite \textit{H. Bauke} and \textit{C. H. Keitel}, Comput. Phys. Commun. 182, No. 12, 2454--2463 (2011; Zbl 1261.65101) Full Text: DOI arXiv OpenURL
Specogna, Ruben; Trevisan, Francesco A discrete geometric approach to solving time independent Schrödinger equation. (English) Zbl 1210.65186 J. Comput. Phys. 230, No. 4, 1370-1381 (2011). MSC: 65N25 35P15 81Q05 35Q40 65N30 PDF BibTeX XML Cite \textit{R. Specogna} and \textit{F. Trevisan}, J. Comput. Phys. 230, No. 4, 1370--1381 (2011; Zbl 1210.65186) Full Text: DOI OpenURL
Furihata, Daisuke; Matsuo, Takayasu Discrete variational derivative method. A structure-preserving numerical method for partial differential equations. (English) Zbl 1227.65094 Chapman & Hall/CRC Numerical Analysis and Scientific Computing. Boca Raton, FL: CRC Press (ISBN 978-1-4200-9445-9/hbk; 978-1-4200-9446-6/ebook). xi, 376 p. (2011). Reviewer: Thomas Sonar (Braunschweig) MSC: 65M60 65M06 65Z05 65-02 35Q35 35Q53 35Q55 00A06 PDF BibTeX XML Cite \textit{D. Furihata} and \textit{T. Matsuo}, Discrete variational derivative method. A structure-preserving numerical method for partial differential equations. Boca Raton, FL: CRC Press (2011; Zbl 1227.65094) Full Text: DOI OpenURL
Amore, Paolo; Fernández, Francisco M.; Hofmann, Christoph P.; Sáenz, Ricardo A. Collocation method for fractional quantum mechanics. (English) Zbl 1314.81061 J. Math. Phys. 51, No. 12, 122101, 16 p. (2010). MSC: 81Q05 35R11 35J10 39A12 65N35 81Q20 PDF BibTeX XML Cite \textit{P. Amore} et al., J. Math. Phys. 51, No. 12, 122101, 16 p. (2010; Zbl 1314.81061) Full Text: DOI arXiv OpenURL
Muminov, M. E. Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice. (English. Russian original) Zbl 1256.81047 Theor. Math. Phys. 164, No. 1, 869-882 (2010); translation from Teor. Mat. Fiz. 164, No. 1, 46-61 (2010). MSC: 81Q10 81Q05 70F07 35J10 47B65 PDF BibTeX XML Cite \textit{M. E. Muminov}, Theor. Math. Phys. 164, No. 1, 869--882 (2010; Zbl 1256.81047); translation from Teor. Mat. Fiz. 164, No. 1, 46--61 (2010) Full Text: DOI OpenURL
Zhao, Jing; Zhou, Ru-Guang An integrable symplectic map related to discrete nonlinear Schrödinger equation. (English) Zbl 1222.81169 Commun. Theor. Phys. 53, No. 5, 799-802 (2010). MSC: 81Q05 35Q55 81R12 81Q10 PDF BibTeX XML Cite \textit{J. Zhao} and \textit{R.-G. Zhou}, Commun. Theor. Phys. 53, No. 5, 799--802 (2010; Zbl 1222.81169) Full Text: DOI OpenURL
Xie, Zheng; Ye, Zheng Numerical solution of Klein-Gordon equation on manifold using DEC. (English) Zbl 1217.81073 Commun. Theor. Phys. 54, No. 2, 287-291 (2010). MSC: 81Q05 81T80 PDF BibTeX XML Cite \textit{Z. Xie} and \textit{Z. Ye}, Commun. Theor. Phys. 54, No. 2, 287--291 (2010; Zbl 1217.81073) Full Text: DOI OpenURL
Antoine, Xavier; Klein, Pauline; Besse, Christophe Open boundary conditions and computational schemes for Schrödinger equations with general potentials and nonlinearities. (English) Zbl 1218.35221 Li, Tatsien (ed.) et al., Some problems on nonlinear hyperbolic equations and applications. Hackensack, NJ: World Scientific; Beijing: Higher Education Press (ISBN 978-981-4322-88-1/hbk). Series in Contemporary Applied Mathematics CAM 15, 3-34 (2010). MSC: 35Q55 65M22 81Q05 PDF BibTeX XML Cite \textit{X. Antoine} et al., Ser. Contemp. Appl. Math. CAM 15, 3--34 (2010; Zbl 1218.35221) OpenURL
Vikram, M.; Baczewski, A.; Shanker, B.; Kempel, L. Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein-Gordon potentials. (English) Zbl 1203.65204 J. Comput. Phys. 229, No. 24, 9119-9134 (2010). MSC: 65M80 35K05 35L15 35L70 65Y20 65T50 PDF BibTeX XML Cite \textit{M. Vikram} et al., J. Comput. Phys. 229, No. 24, 9119--9134 (2010; Zbl 1203.65204) Full Text: DOI OpenURL
Kopylova, E. A. Dispersion estimates for discrete Schrödinger and Klein-Gordon equations. (English. Russian original) Zbl 1213.34110 St. Petersbg. Math. J. 21, No. 5, 743-760 (2010); translation from Algebra Anal. 21, No. 5, 87-113 (2009). Reviewer: Peter Zabreiko (Minsk) MSC: 34L40 47E05 PDF BibTeX XML Cite \textit{E. A. Kopylova}, St. Petersbg. Math. J. 21, No. 5, 743--760 (2010; Zbl 1213.34110); translation from Algebra Anal. 21, No. 5, 87--113 (2009) Full Text: DOI OpenURL