Cai, Jiaxiang; Chen, Juan Efficient dissipation-preserving approaches for the damped nonlinear Schrödinger equation. (English) Zbl 1500.65081 Appl. Numer. Math. 183, 173-185 (2023). MSC: 65M70 65L06 65N35 65T50 65D32 65H10 35Q55 35Q41 82C10 PDF BibTeX XML Cite \textit{J. Cai} and \textit{J. Chen}, Appl. Numer. Math. 183, 173--185 (2023; Zbl 1500.65081) Full Text: DOI OpenURL
Uzunca, Murat; Karasözen, Bülent; Aydın, Ayhan Global energy preserving model reduction for multi-symplectic PDEs. (English) Zbl 07589669 Appl. Math. Comput. 436, Article ID 127483, 21 p. (2023). MSC: 37K05 65M06 65P10 35Q53 35Q55 PDF BibTeX XML Cite \textit{M. Uzunca} et al., Appl. Math. Comput. 436, Article ID 127483, 21 p. (2023; Zbl 07589669) Full Text: DOI arXiv OpenURL
Cuccagna, Scipio; Maeda, Masaya On selection of standing wave at small energy in the 1D cubic Schrödinger equation with a trapping potential. (English) Zbl 07620655 Commun. Math. Phys. 396, No. 3, 1135-1186 (2022). MSC: 35Q55 35C08 35L71 35B40 37K40 PDF BibTeX XML Cite \textit{S. Cuccagna} and \textit{M. Maeda}, Commun. Math. Phys. 396, No. 3, 1135--1186 (2022; Zbl 07620655) Full Text: DOI arXiv OpenURL
Pankov, Alexander; Zhang, Guoping Initial value problem of the discrete nonlinear Schrödinger equation with complex potential. (English) Zbl 07594532 Appl. Anal. 101, No. 16, 5760-5774 (2022). MSC: 37L60 37K60 39A12 35B41 35Q55 PDF BibTeX XML Cite \textit{A. Pankov} and \textit{G. Zhang}, Appl. Anal. 101, No. 16, 5760--5774 (2022; Zbl 07594532) Full Text: DOI OpenURL
Ohta, Yasuhiro; Feng, Bao-Feng General rogue wave solution to the discrete nonlinear Schrödinger equation. (English) Zbl 1497.35439 Physica D 439, Article ID 133400, 11 p. (2022). MSC: 35Q55 37K40 37K10 37K60 39A12 PDF BibTeX XML Cite \textit{Y. Ohta} and \textit{B.-F. Feng}, Physica D 439, Article ID 133400, 11 p. (2022; Zbl 1497.35439) Full Text: DOI arXiv OpenURL
Sun, Hong-Qian; Zhu, Zuo-Nong Darboux transformation and soliton solutions of the spatial discrete coupled complex short pulse equation. (English) Zbl 1495.37061 Physica D 436, Article ID 133312, 13 p. (2022). Reviewer: Ti-Jun Xiao (Fudan) MSC: 37K40 37K35 39A12 39A36 35Q55 PDF BibTeX XML Cite \textit{H.-Q. Sun} and \textit{Z.-N. Zhu}, Physica D 436, Article ID 133312, 13 p. (2022; Zbl 1495.37061) Full Text: DOI OpenURL
Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong From discrete nonlocal nonlinear Schrödinger equation to coupled discrete Heisenberg ferromagnet equation. (English) Zbl 1490.35434 Appl. Math. Lett. 130, Article ID 108002, 7 p. (2022). MSC: 35Q55 35Q41 37K10 37K35 39A12 81T13 82D40 PDF BibTeX XML Cite \textit{L.-Y. Ma} et al., Appl. Math. Lett. 130, Article ID 108002, 7 p. (2022; Zbl 1490.35434) Full Text: DOI arXiv OpenURL
Lin, Genghong; Yu, Jianshe Homoclinic solutions of periodic discrete Schrödinger equations with local superquadratic conditions. (English) Zbl 1491.35405 SIAM J. Math. Anal. 54, No. 2, 1966-2005 (2022). MSC: 35Q55 39A12 39A70 35A01 35B38 35A15 37C29 PDF BibTeX XML Cite \textit{G. Lin} and \textit{J. Yu}, SIAM J. Math. Anal. 54, No. 2, 1966--2005 (2022; Zbl 1491.35405) Full Text: DOI OpenURL
Chen, Guanwei; Schechter, Martin Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms. (English) Zbl 1491.35400 Discrete Contin. Dyn. Syst., Ser. B 27, No. 4, 2107-2114 (2022). MSC: 35Q55 39A12 39A70 35B40 34B20 37K60 PDF BibTeX XML Cite \textit{G. Chen} and \textit{M. Schechter}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 4, 2107--2114 (2022; Zbl 1491.35400) Full Text: DOI OpenURL
Danesi, Veronica; Sansottera, Marco; Paleari, Simone; Penati, Tiziano Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms. (English) Zbl 1491.37063 Commun. Nonlinear Sci. Numer. Simul. 108, Article ID 106266, 23 p. (2022). MSC: 37K60 37K55 35Q55 PDF BibTeX XML Cite \textit{V. Danesi} et al., Commun. Nonlinear Sci. Numer. Simul. 108, Article ID 106266, 23 p. (2022; Zbl 1491.37063) Full Text: DOI arXiv OpenURL
Arezzo, Claudio; Balducci, Federico; Piergallini, Riccardo; Scardicchio, Antonello; Vanoni, Carlo Localization in the discrete non-linear Schrödinger equation and geometric properties of the microcanonical surface. (English) Zbl 1489.82049 J. Stat. Phys. 186, No. 2, Paper No. 24, 23 p. (2022). MSC: 82C20 82C26 82C27 81V70 35Q55 35Q70 PDF BibTeX XML Cite \textit{C. Arezzo} et al., J. Stat. Phys. 186, No. 2, Paper No. 24, 23 p. (2022; Zbl 1489.82049) Full Text: DOI arXiv OpenURL
Jafarov, E. I.; Nagiyev, S. M. Effective mass of the discrete values as a hidden feature of the one-dimensional harmonic oscillator model: exact solution of the Schrödinger equation with a mass varying by position. (English) Zbl 1489.81026 Mod. Phys. Lett. A 36, No. 29, Article ID 2150206, 12 p. (2021). MSC: 81Q05 35Q41 33C45 81T12 35P15 81Q80 34C15 PDF BibTeX XML Cite \textit{E. I. Jafarov} and \textit{S. M. Nagiyev}, Mod. Phys. Lett. A 36, No. 29, Article ID 2150206, 12 p. (2021; Zbl 1489.81026) Full Text: DOI OpenURL
Pereira, Jardel Pullback attractor for a nonlocal discrete nonlinear Schrödinger equation with delays. (English) Zbl 1499.35558 Electron. J. Qual. Theory Differ. Equ. 2021, Paper No. 93, 18 p. (2021). MSC: 35Q55 37L60 37B55 37L30 PDF BibTeX XML Cite \textit{J. Pereira}, Electron. J. Qual. Theory Differ. Equ. 2021, Paper No. 93, 18 p. (2021; Zbl 1499.35558) Full Text: DOI OpenURL
Zhao, Xiaofei Numerical integrators for continuous disordered nonlinear Schrödinger equation. (English) Zbl 1482.35222 J. Sci. Comput. 89, No. 2, Paper No. 40, 27 p. (2021). MSC: 35Q55 35Q41 35B65 65L20 65L70 65M06 65M12 65M15 65T50 65P10 60H40 82C44 35R60 PDF BibTeX XML Cite \textit{X. Zhao}, J. Sci. Comput. 89, No. 2, Paper No. 40, 27 p. (2021; Zbl 1482.35222) Full Text: DOI arXiv OpenURL
Ross, R. M.; Kevrekidis, P. G.; Pelinovsky, D. E. Localization in optical systems with an intensity-dependent dispersion. (English) Zbl 1479.35820 Q. Appl. Math. 79, No. 4, 641-665 (2021). MSC: 35Q55 35Q41 35Q60 78A60 35P15 35C08 35B65 35B40 65M70 65L06 65T50 65H10 PDF BibTeX XML Cite \textit{R. M. Ross} et al., Q. Appl. Math. 79, No. 4, 641--665 (2021; Zbl 1479.35820) Full Text: DOI arXiv OpenURL
Li, Xueyang; Jiang, Kai Numerical simulation for quasiperiodic quantum dynamical systems. (Chinese. English summary) Zbl 1488.81002 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 1488.81002) Full Text: DOI OpenURL
Chen, Guanwei; Ma, Shiwang Perturbed Schrödinger lattice systems with superlinear terms: multiplicity of homoclinic solutions. (English) Zbl 1473.37095 Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 185, 15 p. (2021). MSC: 37K60 35Q55 39A12 70K44 PDF BibTeX XML Cite \textit{G. Chen} and \textit{S. Ma}, Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 185, 15 p. (2021; Zbl 1473.37095) Full Text: DOI OpenURL
Biondini, Gino; Li, Sitai; Mantzavinos, Dionyssios Long-time asymptotics for the focusing nonlinear Schrödinger equation with nonzero boundary conditions in the presence of a discrete spectrum. (English) Zbl 1464.35309 Commun. Math. Phys. 382, No. 3, 1495-1577 (2021). MSC: 35Q55 35A22 35P25 35G10 35K25 35B40 35C08 35B34 37K15 PDF BibTeX XML Cite \textit{G. Biondini} et al., Commun. Math. Phys. 382, No. 3, 1495--1577 (2021; Zbl 1464.35309) Full Text: DOI arXiv OpenURL
Zhu, Qing; Zhou, Zhan; Wang, Lin Existence and stability of discrete solitons in nonlinear Schrödinger lattices with hard potentials. (English) Zbl 1490.35466 Physica D 403, Article ID 132326, 10 p. (2020). MSC: 35Q55 35Q51 39A12 37K40 37K60 PDF BibTeX XML Cite \textit{Q. Zhu} et al., Physica D 403, Article ID 132326, 10 p. (2020; Zbl 1490.35466) 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
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
Van Gorder, Robert A.; Krause, Andrew L.; Malomed, Boris A.; Kaup, D. J. Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices. (English) Zbl 1453.82047 Commun. Nonlinear Sci. Numer. Simul. 85, Article ID 105244, 14 p. (2020). MSC: 82C20 35Q55 35Q41 35C08 82C10 35A15 78A50 78A60 PDF BibTeX XML Cite \textit{R. A. Van Gorder} et al., Commun. Nonlinear Sci. Numer. Simul. 85, Article ID 105244, 14 p. (2020; Zbl 1453.82047) Full Text: DOI arXiv OpenURL
Jiao, Ruiyun; Zhang, Wenqian; Yang, Zhendong; Wang, Jing; Zhan, Kaiyun; Liu, Bing Conical diffraction modulation in honeycomb lattices. (English) Zbl 1451.78038 Commun. Nonlinear Sci. Numer. Simul. 84, Article ID 105168, 10 p. (2020). MSC: 78A60 78A40 78M99 65T50 82B20 82D80 35Q41 35Q55 PDF BibTeX XML Cite \textit{R. Jiao} et al., Commun. Nonlinear Sci. Numer. Simul. 84, Article ID 105168, 10 p. (2020; Zbl 1451.78038) 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
Huh, Hyungjin; Hussain, Swaleh; Pelinovsky, Dmitry E. Chern-Simons-Schrödinger theory on a one-dimensional lattice. (English) Zbl 1446.35183 Lett. Math. Phys. 110, No. 8, 2221-2244 (2020). MSC: 35Q55 35Q40 70S15 81T13 35A01 35A02 35C08 PDF BibTeX XML Cite \textit{H. Huh} et al., Lett. Math. Phys. 110, No. 8, 2221--2244 (2020; Zbl 1446.35183) 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
He, Zhu; Cai, Jiaxiang; Shen, Bangyu Decoupled conservative schemes for computing dynamics of the strongly coupled nonlinear Schrödinger system. (English) Zbl 1448.37105 Appl. Numer. Math. 157, 276-290 (2020). MSC: 37M15 65P10 35Q55 PDF BibTeX XML Cite \textit{Z. He} et al., Appl. Numer. Math. 157, 276--290 (2020; Zbl 1448.37105) 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
Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H. Discrete nonlocal nonlinear Schrödinger systems: integrability, inverse scattering and solitons. (English) Zbl 1446.37062 Nonlinearity 33, No. 7, 3653-3707 (2020). Reviewer: Eszter Gselmann (Debrecen) MSC: 37K15 37K60 39A36 39A12 35Q55 PDF BibTeX XML Cite \textit{M. J. Ablowitz} et al., Nonlinearity 33, No. 7, 3653--3707 (2020; Zbl 1446.37062) Full Text: DOI OpenURL
Cai, Jiaxiang; Zhang, Haihui Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions. (English) Zbl 1465.65067 Appl. Math. Lett. 102, Article ID 106158, 7 p. (2020). MSC: 65M06 65M20 65T50 65H10 65P10 35Q55 PDF BibTeX XML Cite \textit{J. Cai} and \textit{H. Zhang}, Appl. Math. Lett. 102, Article ID 106158, 7 p. (2020; Zbl 1465.65067) Full Text: DOI OpenURL
Chen, Guanwei; Ma, Shiwang Perturbed Schrödinger lattice systems: existence of homoclinic solutions. (English) Zbl 1437.35618 Proc. R. Soc. Edinb., Sect. A, Math. 149, No. 4, 1083-1096 (2019). MSC: 35Q55 39A12 39A70 PDF BibTeX XML Cite \textit{G. Chen} and \textit{S. Ma}, Proc. R. Soc. Edinb., Sect. A, Math. 149, No. 4, 1083--1096 (2019; Zbl 1437.35618) Full Text: DOI OpenURL
Hanif, Y.; Saleem, U. Broken and unbroken \(\mathcal{PT}\)-symmetric solutions of semi-discrete nonlocal nonlinear Schrödinger equation. (English) Zbl 1430.37084 Nonlinear Dyn. 98, No. 1, 233-244 (2019). MSC: 37K40 35Q55 37K35 35B06 PDF BibTeX XML Cite \textit{Y. Hanif} and \textit{U. Saleem}, Nonlinear Dyn. 98, No. 1, 233--244 (2019; Zbl 1430.37084) Full Text: DOI OpenURL
Yamane, Hideshi Asymptotics for the focusing integrable discrete nonlinear Schrödinger equation. (English) Zbl 1434.35198 RIMS Kôkyûroku Bessatsu B75, 31-39 (2019). MSC: 35Q55 35Q15 35B40 35C08 37K10 PDF BibTeX XML Cite \textit{H. Yamane}, RIMS Kôkyûroku Bessatsu B75, 31--39 (2019; Zbl 1434.35198) OpenURL
Chen, Guanwei; Schechter, Martin Multiple solutions for non-periodic Schrödinger lattice systems with perturbation and super-linear terms. (English) Zbl 1431.35167 Z. Angew. Math. Phys. 70, No. 5, Paper No. 152, 9 p. (2019). Reviewer: Jipeng Cheng (Xuzhou) MSC: 35Q55 35Q51 39A12 39A70 PDF BibTeX XML Cite \textit{G. Chen} and \textit{M. Schechter}, Z. Angew. Math. Phys. 70, No. 5, Paper No. 152, 9 p. (2019; Zbl 1431.35167) Full Text: DOI OpenURL
Alfimov, G. L.; Korobeinikov, A. S.; Lustri, C. J.; Pelinovsky, D. E. Standing lattice solitons in the discrete NLS equation with saturation. (English) Zbl 1423.34019 Nonlinearity 32, No. 9, 3445-3484 (2019). MSC: 34A33 34M35 34M40 37K40 39A10 PDF BibTeX XML Cite \textit{G. L. Alfimov} et al., Nonlinearity 32, No. 9, 3445--3484 (2019; Zbl 1423.34019) Full Text: DOI arXiv OpenURL
Hirose, Sampei; Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro Discrete local induction equation. (English) Zbl 1422.37046 J. Integrable Syst. 4, Article ID xyz003, 43 p. (2019). MSC: 37K10 39A12 35Q55 PDF BibTeX XML Cite \textit{S. Hirose} et al., J. Integrable Syst. 4, Article ID xyz003, 43 p. (2019; Zbl 1422.37046) Full Text: DOI arXiv OpenURL
Assainova, O.; Klein, C.; McLaughlin, K. D. T.-R.; Miller, P. D. A study of the direct spectral transform for the defocusing Davey-Stewartson II equation the semiclassical limit. (English) Zbl 1420.35339 Commun. Pure Appl. Math. 72, No. 7, 1474-1547 (2019). MSC: 35Q55 37K15 35Q41 35C05 65T50 35B40 35B25 PDF BibTeX XML Cite \textit{O. Assainova} et al., Commun. Pure Appl. Math. 72, No. 7, 1474--1547 (2019; Zbl 1420.35339) Full Text: DOI arXiv OpenURL
Liao, Feng; Zhang, Luming; Hu, Xiuling Conservative finite difference methods for fractional Schrödinger-Boussinesq equations and convergence analysis. (English) Zbl 1418.65103 Numer. Methods Partial Differ. Equations 35, No. 4, 1305-1325 (2019). MSC: 65M06 65M12 35R11 35Q55 35Q82 82D10 65H10 65F05 65M15 PDF BibTeX XML Cite \textit{F. Liao} et al., Numer. Methods Partial Differ. Equations 35, No. 4, 1305--1325 (2019; Zbl 1418.65103) Full Text: DOI OpenURL
Geng, Xianguo; Zeng, Xin; Wei, Jiao The application of the theory of trigonal curves to the discrete coupled nonlinear Schrödinger hierarchy. (English) Zbl 1421.35335 Ann. Henri Poincaré 20, No. 8, 2585-2621 (2019). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q55 35Q41 37K10 35Q51 35C08 PDF BibTeX XML Cite \textit{X. Geng} et al., Ann. Henri Poincaré 20, No. 8, 2585--2621 (2019; Zbl 1421.35335) Full Text: DOI OpenURL
Bernier, Joackim Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on \( h\mathbb{Z}\). (English) Zbl 1433.35355 Discrete Contin. Dyn. Syst. 39, No. 6, 3179-3195 (2019). Reviewer: Johanna Michor (Wien) MSC: 35Q55 37K60 65P99 35Q41 PDF BibTeX XML Cite \textit{J. Bernier}, Discrete Contin. Dyn. Syst. 39, No. 6, 3179--3195 (2019; Zbl 1433.35355) Full Text: DOI arXiv OpenURL
Zhou, Tao; Liu, Xia; Shi, Haiping; Wen, Zongliang Existence of multiple breathers for discrete nonlinear Schrödinger equations. (English) Zbl 1408.39006 Electron. J. Differ. Equ. 2019, Paper No. 27, 12 p. (2019). MSC: 39A12 39A70 39A14 37K40 35Q55 PDF BibTeX XML Cite \textit{T. Zhou} et al., Electron. J. Differ. Equ. 2019, Paper No. 27, 12 p. (2019; Zbl 1408.39006) Full Text: Link OpenURL
Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model. (English) Zbl 1405.60070 ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 1, 179-209 (2019). MSC: 60G60 60G42 82B44 PDF BibTeX XML Cite \textit{M. Disertori} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 1, 179--209 (2019; Zbl 1405.60070) Full Text: arXiv Link OpenURL
Mu, Zhenguo; Li, Haochen; Wang, Yushun; Cai, Wenjun A Galerkin splitting symplectic method for the two dimensional nonlinear Schrödinger equation. (English) Zbl 1488.65450 Adv. Appl. Math. Mech. 10, No. 5, 1069-1089 (2018). MSC: 65M60 65M06 65M20 65M70 65N30 65P10 65T50 35Q55 35Q41 PDF BibTeX XML Cite \textit{Z. Mu} et al., Adv. Appl. Math. Mech. 10, No. 5, 1069--1089 (2018; Zbl 1488.65450) Full Text: DOI OpenURL
Biskup, Marek; Fukushima, Ryoki; König, Wolfgang Eigenvalue fluctuations for lattice Anderson Hamiltonians: unbounded potentials. (English) Zbl 1482.35147 Interdiscip. Inf. Sci. 24, No. 1, 59-76 (2018). MSC: 35P20 35J10 35R60 39A12 60H25 82B44 74Q15 47A75 47H40 PDF BibTeX XML Cite \textit{M. Biskup} et al., Interdiscip. Inf. Sci. 24, No. 1, 59--76 (2018; Zbl 1482.35147) Full Text: DOI arXiv OpenURL
Prykarpatski, Anatolij New integrable differential-difference and fractional nonlinear dynamical systems and their algebro-analytical properties. (English) Zbl 07265273 Commun. Nonlinear Sci. Numer. Simul. 64, 256-268 (2018). MSC: 35A30 35G25 35N10 37K35 58J70 58J72 34A34 PDF BibTeX XML Cite \textit{A. Prykarpatski}, Commun. Nonlinear Sci. Numer. Simul. 64, 256--268 (2018; Zbl 07265273) Full Text: DOI OpenURL
Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin Matter-wave solitons supported by quadrupole-quadrupole interactions and anisotropic discrete lattices. (English) Zbl 1423.82006 Int. J. Mod. Phys. B 32, No. 9, Article ID 1850107, 14 p. (2018). MSC: 82B20 35Q55 PDF BibTeX XML Cite \textit{R.-X. Zhong} et al., Int. J. Mod. Phys. B 32, No. 9, Article ID 1850107, 14 p. (2018; Zbl 1423.82006) Full Text: DOI OpenURL
Cai, Jiaxiang; Bai, Chuanzhi; Zhang, Haihui Decoupled local/global energy-preserving schemes for the \(N\)-coupled nonlinear Schrödinger equations. (English) Zbl 1416.65510 J. Comput. Phys. 374, 281-299 (2018). MSC: 65P10 35Q55 65T50 PDF BibTeX XML Cite \textit{J. Cai} et al., J. Comput. Phys. 374, 281--299 (2018; Zbl 1416.65510) Full Text: DOI OpenURL
Guo, Feng A local energy conservative scheme for nonlinear coupled Schrödinger-KdV equations. (Chinese. English summary) Zbl 1424.65128 Math. Numer. Sin. 40, No. 3, 313-324 (2018). MSC: 65M06 35L65 65P10 35Q53 35Q55 PDF BibTeX XML Cite \textit{F. Guo}, Math. Numer. Sin. 40, No. 3, 313--324 (2018; Zbl 1424.65128) OpenURL
Karasözen, Bülent; Uzunca, Murat Energy preserving model order reduction of the nonlinear Schrödinger equation. (English) Zbl 1404.65310 Adv. Comput. Math. 44, No. 6, 1769-1796 (2018). MSC: 65P10 65M60 35Q55 37M15 93A15 PDF BibTeX XML Cite \textit{B. Karasözen} and \textit{M. Uzunca}, Adv. Comput. Math. 44, No. 6, 1769--1796 (2018; Zbl 1404.65310) Full Text: DOI arXiv OpenURL
de la Hoz, Francisco; Vega, Luis On the relationship between the one-corner problem and the \(M\)-corner problem for the vortex filament equation. (English) Zbl 1447.35263 J. Nonlinear Sci. 28, No. 6, 2275-2327 (2018). MSC: 35Q35 35K40 28A80 35Q55 65M70 65T50 76B47 65L06 76M23 PDF BibTeX XML Cite \textit{F. de la Hoz} and \textit{L. Vega}, J. Nonlinear Sci. 28, No. 6, 2275--2327 (2018; Zbl 1447.35263) Full Text: DOI arXiv OpenURL
Tsoy, E. N.; Umarov, B. A. Introduction to nonlinear discrete systems: theory and modelling. (English) Zbl 1396.39006 Eur. J. Phys. 39, No. 5, Article ID 055803, 13 p. (2018). MSC: 39A12 35Q55 82C20 82D25 82D77 35C08 97M50 PDF BibTeX XML Cite \textit{E. N. Tsoy} and \textit{B. A. Umarov}, Eur. J. Phys. 39, No. 5, Article ID 055803, 13 p. (2018; Zbl 1396.39006) Full Text: DOI arXiv Link OpenURL
Zhao, Hai-qiong; Yuan, Jinyun; Zhu, Zuo-nong Integrable semi-discrete Kundu-Eckhaus equation: Darboux transformation, breather, rogue wave and continuous limit theory. (English) Zbl 1383.37059 J. Nonlinear Sci. 28, No. 1, 43-68 (2018). MSC: 37K10 37K40 34K25 35Q55 37K35 34K31 PDF BibTeX XML Cite \textit{H.-q. Zhao} et al., J. Nonlinear Sci. 28, No. 1, 43--68 (2018; Zbl 1383.37059) Full Text: DOI OpenURL
Wu, Xiao-Yu; Tian, Bo; Liu, Lei; Sun, Yan Bright and dark solitons for a discrete (2+1)-dimensional Ablowitz-Ladik equation for the nonlinear optics and Bose-Einstein condensation. (English) Zbl 1448.81535 Commun. Nonlinear Sci. Numer. Simul. 50, 201-210 (2017). MSC: 81V80 81V73 35Q55 35C08 82B26 78A60 39A12 68W30 PDF BibTeX XML Cite \textit{X.-Y. Wu} et al., Commun. Nonlinear Sci. Numer. Simul. 50, 201--210 (2017; Zbl 1448.81535) Full Text: DOI OpenURL
Ma, Li-Yuan; Zhu, Zuo-Nong Spatial properties and numerical solitary waves of a nonintegrable discrete nonlinear Schrödinger equation with nonlinear hopping. (English) Zbl 1411.35242 Appl. Math. Comput. 309, 93-106 (2017). MSC: 35Q55 35C08 37K40 37M05 65L60 PDF BibTeX XML Cite \textit{L.-Y. Ma} and \textit{Z.-N. Zhu}, Appl. Math. Comput. 309, 93--106 (2017; Zbl 1411.35242) Full Text: DOI OpenURL
Zeidabadi, Fatemeh Ahmadi; Hoseini, Seyed Mohammad Solitons for nearly integrable bright spinor Bose-Einstein condensate. (English) Zbl 1407.37106 Bull. Iran. Math. Soc. 43, No. 3, 665-681 (2017). MSC: 37K40 37K10 35Q55 35Q51 PDF BibTeX XML Cite \textit{F. A. Zeidabadi} and \textit{S. M. Hoseini}, Bull. Iran. Math. Soc. 43, No. 3, 665--681 (2017; Zbl 1407.37106) Full Text: Link OpenURL
Yu, Fajun Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with \(\mathcal{P} \mathcal{T}\)-symmetric potential. (English) Zbl 1390.35345 Chaos 27, No. 2, 023108, 12 p. (2017). MSC: 35Q55 39A14 39A12 35C08 37B55 PDF BibTeX XML Cite \textit{F. Yu}, Chaos 27, No. 2, 023108, 12 p. (2017; Zbl 1390.35345) Full Text: DOI OpenURL
Yamane, Hideshi Asymptotic analysis based on the inverse scattering method. (English) Zbl 1391.35361 RIMS Kôkyûroku Bessatsu B63, 1-11 (2017). MSC: 35Q55 35Q15 37K15 35B40 PDF BibTeX XML Cite \textit{H. Yamane}, RIMS Kôkyûroku Bessatsu B63, 1--11 (2017; Zbl 1391.35361) OpenURL
Spohn, Herbert The Kardar-Parisi-Zhang equation: a statistical physics perspective. (English) Zbl 1403.35295 Schehr, Grégory (ed.) et al., Stochastic processes and random matrices. Lecture notes of the Les Houches summer school. Volume 104, Les Houches, France, July 6–31, 2015. Oxford: Oxford University Press (ISBN 978-0-19-879731-9/hbk). 177-227 (2017). Reviewer: Giovanni Mascali (Arcavacata di Rende) MSC: 35Q82 82C24 82C22 60H15 82D60 35Q55 PDF BibTeX XML Cite \textit{H. Spohn}, in: Stochastic processes and random matrices. Lecture notes of the Les Houches summer school. Volume 104, Les Houches, France, July 6--31, 2015. Oxford: Oxford University Press. 177--227 (2017; Zbl 1403.35295) Full Text: DOI arXiv OpenURL
Hao, Hui-Qin; Guo, Rui; Zhang, Jian-Wen Modulation instability, conservation laws and soliton solutions for an inhomogeneous discrete nonlinear Schrödinger equation. (English) Zbl 1380.37135 Nonlinear Dyn. 88, No. 3, 1615-1622 (2017). MSC: 37K60 37K10 35C08 PDF BibTeX XML Cite \textit{H.-Q. Hao} et al., Nonlinear Dyn. 88, No. 3, 1615--1622 (2017; Zbl 1380.37135) Full Text: DOI OpenURL
Babalic, Corina N.; Carstea, A. S. Coupled Ablowitz-Ladik equations with branched dispersion. (English) Zbl 1386.37067 J. Phys. A, Math. Theor. 50, No. 41, Article ID 415201, 13 p. (2017). Reviewer: Ti-Jun Xiao (Fudan) MSC: 37K10 35C08 35Q55 34K31 PDF BibTeX XML Cite \textit{C. N. Babalic} and \textit{A. S. Carstea}, J. Phys. A, Math. Theor. 50, No. 41, Article ID 415201, 13 p. (2017; Zbl 1386.37067) Full Text: DOI arXiv OpenURL
Jia, Liqian; Chen, Guanwei Discrete Schrödinger equations with sign-changing nonlinearities: infinitely many homoclinic solutions. (English) Zbl 1372.39011 J. Math. Anal. Appl. 452, No. 1, 568-577 (2017). MSC: 39A12 35Q55 37C29 PDF BibTeX XML Cite \textit{L. Jia} and \textit{G. Chen}, J. Math. Anal. Appl. 452, No. 1, 568--577 (2017; Zbl 1372.39011) Full Text: DOI OpenURL
Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. A supersymmetric approach to martingales related to the vertex-reinforced jump process. (English) Zbl 1364.60068 ALEA, Lat. Am. J. Probab. Math. Stat. 14, No. 1, 529-555 (2017). MSC: 60G60 60G42 82B44 PDF BibTeX XML Cite \textit{M. Disertori} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 14, No. 1, 529--555 (2017; Zbl 1364.60068) Full Text: arXiv Link OpenURL
Adamopoulou, Panagiota; Doikou, Anastasia; Papamikos, Georgios Darboux-Bäcklund transformations, dressing & impurities in multi-component NLS. (English) Zbl 1360.35236 Nucl. Phys., B 918, 91-114 (2017). MSC: 35Q55 39A12 37K35 35P30 PDF BibTeX XML Cite \textit{P. Adamopoulou} et al., Nucl. Phys., B 918, 91--114 (2017; Zbl 1360.35236) Full Text: DOI arXiv OpenURL
Jenkinson, M.; Weinstein, M. I. Discrete solitary waves in systems with nonlocal interactions and the Peierls-Nabarro barrier. (English) Zbl 1397.35276 Commun. Math. Phys. 351, No. 1, 45-94 (2017). Reviewer: Gilles Evéquoz (Delémont) MSC: 35Q55 35C08 35B32 82B20 35R11 35C20 PDF BibTeX XML Cite \textit{M. Jenkinson} and \textit{M. I. Weinstein}, Commun. Math. Phys. 351, No. 1, 45--94 (2017; Zbl 1397.35276) Full Text: DOI arXiv OpenURL
Yamane, Hideshi Asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation. (English) Zbl 1360.35257 RIMS Kôkyûroku Bessatsu B57, 15-25 (2016). MSC: 35Q55 35Q15 35B40 37K15 35Q53 41A60 PDF BibTeX XML Cite \textit{H. Yamane}, RIMS Kôkyûroku Bessatsu B57, 15--25 (2016; Zbl 1360.35257) OpenURL
Yoshimura, Kazuyuki Existence of discrete solitons in discrete nonlinear Schrödinger equations with non-weak couplings. (English) Zbl 1352.37183 Japan J. Ind. Appl. Math. 33, No. 2, 379-400 (2016). MSC: 37K60 35Q55 37K40 39A12 39A14 PDF BibTeX XML Cite \textit{K. Yoshimura}, Japan J. Ind. Appl. Math. 33, No. 2, 379--400 (2016; Zbl 1352.37183) Full Text: DOI OpenURL
Guo, Rui; Zhao, Xiao-Juan Discrete Hirota equation: discrete Darboux transformation and new discrete soliton solutions. (English) Zbl 1355.37085 Nonlinear Dyn. 84, No. 4, 1901-1907 (2016). MSC: 37K10 37K30 35Q53 35Q55 39A14 PDF BibTeX XML Cite \textit{R. Guo} and \textit{X.-J. Zhao}, Nonlinear Dyn. 84, No. 4, 1901--1907 (2016; Zbl 1355.37085) Full Text: DOI OpenURL
Fritzsche, B.; Kaashoek, M. A.; Kirstein, B.; Sakhnovich, A. L. Skew-selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations. (English) Zbl 1376.37111 Math. Nachr. 289, No. 14-15, 1792-1819 (2016). MSC: 37K10 34B20 35Q55 39A12 35R30 34L40 PDF BibTeX XML Cite \textit{B. Fritzsche} et al., Math. Nachr. 289, No. 14--15, 1792--1819 (2016; Zbl 1376.37111) Full Text: DOI arXiv OpenURL
Pelinovsky, Dmitry; Penati, Tiziano; Paleari, Simone Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrödinger equations. (English) Zbl 1347.37123 Rev. Math. Phys. 28, No. 7, Article ID 1650015, 25 p. (2016). MSC: 37K60 37K40 37K55 70K45 35Q55 PDF BibTeX XML Cite \textit{D. Pelinovsky} et al., Rev. Math. Phys. 28, No. 7, Article ID 1650015, 25 p. (2016; Zbl 1347.37123) Full Text: DOI arXiv OpenURL
Chvartatskyi, Oleksandr; Dimakis, Aristophanes; Müller-Hoissen, Folkert Self-consistent sources for integrable equations via deformations of binary Darboux transformations. (English) Zbl 1346.35040 Lett. Math. Phys. 106, No. 8, 1139-1179 (2016). MSC: 35C08 37K10 70H06 PDF BibTeX XML Cite \textit{O. Chvartatskyi} et al., Lett. Math. Phys. 106, No. 8, 1139--1179 (2016; Zbl 1346.35040) Full Text: DOI arXiv OpenURL
Ma, Li-Yuan; Zhu, Zuo-Nong Nonlocal nonlinear Schrödinger equation and its discrete version: soliton solutions and gauge equivalence. (English) Zbl 1352.35163 J. Math. Phys. 57, No. 8, 083507, 20 p. (2016). Reviewer: Xue Bo (Zhengzhou) MSC: 35Q55 39A12 35C08 70S15 35Q51 37K35 PDF BibTeX XML Cite \textit{L.-Y. Ma} and \textit{Z.-N. Zhu}, J. Math. Phys. 57, No. 8, 083507, 20 p. (2016; Zbl 1352.35163) Full Text: DOI arXiv OpenURL
Chen, Junchao; Chen, Yong; Feng, Bao-Feng; Maruno, Ken-Ichi; Ohta, Yasuhiro An integrable semi-discretization of the coupled Yajima-Oikawa system. (English) Zbl 1343.37063 J. Phys. A, Math. Theor. 49, No. 16, Article ID 165201, 19 p. (2016). MSC: 37K10 35Q53 35Q55 39A12 35C08 PDF BibTeX XML Cite \textit{J. Chen} et al., J. Phys. A, Math. Theor. 49, No. 16, Article ID 165201, 19 p. (2016; Zbl 1343.37063) Full Text: DOI arXiv OpenURL
Zhao, Hai-qiong; Yuan, Jinyun A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system. (English) Zbl 1342.35361 J. Phys. A, Math. Theor. 49, No. 27, Article ID 275204, 17 p. (2016). MSC: 35Q55 35G50 PDF BibTeX XML Cite \textit{H.-q. Zhao} and \textit{J. Yuan}, J. Phys. A, Math. Theor. 49, No. 27, Article ID 275204, 17 p. (2016; Zbl 1342.35361) Full Text: DOI OpenURL
Habibullin, I. T.; Khakimova, A. R.; Poptsova, M. N. On a method for constructing the Lax pairs for nonlinear integrable equations. (English) Zbl 1359.37133 J. Phys. A, Math. Theor. 49, No. 3, Article ID 035202, 35 p. (2016). MSC: 37K10 35Q55 37K05 PDF BibTeX XML Cite \textit{I. T. Habibullin} et al., J. Phys. A, Math. Theor. 49, No. 3, Article ID 035202, 35 p. (2016; Zbl 1359.37133) Full Text: DOI arXiv OpenURL
Klopp, Frédéric Resonances for large one-dimensional “ergodic” systems. (English. French summary) Zbl 1348.35210 Anal. PDE 9, No. 2, 259-352 (2016). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q40 35B34 47B80 47H40 60H25 82B44 PDF BibTeX XML Cite \textit{F. Klopp}, Anal. PDE 9, No. 2, 259--352 (2016; Zbl 1348.35210) Full Text: DOI arXiv OpenURL
Ma, Li-Yuan; Zhu, Zuo-Nong \(N\)-soliton solution for an integrable nonlocal discrete focusing nonlinear Schrödinger equation. (English) Zbl 1342.35346 Appl. Math. Lett. 59, 115-121 (2016). MSC: 35Q55 35C08 37K10 35B10 PDF BibTeX XML Cite \textit{L.-Y. Ma} and \textit{Z.-N. Zhu}, Appl. Math. Lett. 59, 115--121 (2016; Zbl 1342.35346) Full Text: DOI OpenURL
Jenkinson, M.; Weinstein, M. I. Onsite and offsite bound states of the discrete nonlinear Schrödinger equation and the Peierls-Nabarro barrier. (English) Zbl 1357.37087 Nonlinearity 29, No. 1, 27-86 (2016). MSC: 37L60 39A22 35Q55 39A14 PDF BibTeX XML Cite \textit{M. Jenkinson} and \textit{M. I. Weinstein}, Nonlinearity 29, No. 1, 27--86 (2016; Zbl 1357.37087) Full Text: DOI arXiv OpenURL
van der Mee, Cornelis Inverse scattering transform for the discrete focusing nonlinear Schrödinger equation with nonvanishing boundary conditions. (English) Zbl 1420.37101 J. Nonlinear Math. Phys. 22, No. 2, 233-264 (2015). MSC: 37K15 35Q55 39A70 PDF BibTeX XML Cite \textit{C. van der Mee}, J. Nonlinear Math. Phys. 22, No. 2, 233--264 (2015; Zbl 1420.37101) Full Text: DOI Link OpenURL
Tchinang Tchameu, J. D.; Tchawoua, C.; Togueu Motcheyo, A. B. Effects of next-nearest-neighbor interactions on discrete multibreathers corresponding to Davydov model with saturable nonlinearities. (English) Zbl 1349.35356 Phys. Lett., A 379, No. 45-46, 2984-2990 (2015). MSC: 35Q55 37K45 37K40 PDF BibTeX XML Cite \textit{J. D. Tchinang Tchameu} et al., Phys. Lett., A 379, No. 45--46, 2984--2990 (2015; Zbl 1349.35356) Full Text: DOI OpenURL
Gegenhasi; Manduhu; Ye, Xiaohan On the fully discrete Davey-Stewartson system with self-consistent sources. (English) Zbl 1354.39004 Pac. J. Appl. Math. 7, No. 3, 163-175 (2015). MSC: 39A12 35Q55 37K10 PDF BibTeX XML Cite \textit{Gegenhasi} et al., Pac. J. Appl. Math. 7, No. 3, 163--175 (2015; Zbl 1354.39004) OpenURL
Konstantinou-Rizos, S.; Mikhailov, A. V.; Xenitidis, P. Reduction groups and related integrable difference systems of nonlinear Schrödinger type. (English) Zbl 1328.35213 J. Math. Phys. 56, No. 8, 082701, 21 p. (2015). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 39A12 37K35 PDF BibTeX XML Cite \textit{S. Konstantinou-Rizos} et al., J. Math. Phys. 56, No. 8, 082701, 21 p. (2015; Zbl 1328.35213) Full Text: DOI arXiv OpenURL
Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro Integrable semi-discretization of a multi-component short pulse equation. (English) Zbl 1315.35201 J. Math. Phys. 56, No. 4, 043502, 15 p. (2015). MSC: 35Q55 78A60 81V80 35Q60 35C08 37K20 37K35 39A12 PDF BibTeX XML Cite \textit{B.-F. Feng} et al., J. Math. Phys. 56, No. 4, 043502, 15 p. (2015; Zbl 1315.35201) Full Text: DOI arXiv OpenURL
Jiang, Chaolong; Huang, Rongfang; Sun, Jianqiang The averaged discrete gradient method for the coupled nonlinear Schrödinger equations. (Chinese. English summary) Zbl 1324.65153 Chin. J. Eng. Math. 31, No. 5, 707-718 (2014). MSC: 65P10 35Q55 37M15 37K10 65M60 PDF BibTeX XML Cite \textit{C. Jiang} et al., Chin. J. Eng. Math. 31, No. 5, 707--718 (2014; Zbl 1324.65153) Full Text: DOI OpenURL
Li, Qi; Duan, Qiu-Yuan; Chen, Deng-Yuan; Zhang, Jian-Bing Exact solutions of Ablowitz-Ladik hierarchy with self-consistent sources revisited and reductions. (English) Zbl 1294.37028 Commun. Theor. Phys. 62, No. 1, 5-12 (2014). MSC: 37K10 35C08 35Q51 35Q53 35Q55 PDF BibTeX XML Cite \textit{Q. Li} et al., Commun. Theor. Phys. 62, No. 1, 5--12 (2014; Zbl 1294.37028) Full Text: DOI OpenURL
Yang, Xinbo; Zhao, Caidi; Cao, Juan Dynamics of the discrete coupled nonlinear Schrödinger-Boussinesq equations. (English) Zbl 1291.39019 Appl. Math. Comput. 219, No. 16, 8508-8524 (2013). MSC: 39A12 35Q55 37C70 37A35 PDF BibTeX XML Cite \textit{X. Yang} et al., Appl. Math. Comput. 219, No. 16, 8508--8524 (2013; Zbl 1291.39019) Full Text: DOI OpenURL
Wen, Xiao-Yong; Wang, Deng-Shan; Meng, Xiang-Hua \(N\)-soliton solutions and inelastic interaction for a discretized second-order in time nonlinear Schrödinger equation. (English) Zbl 1396.37076 Rep. Math. Phys. 72, No. 3, 349-367 (2013). MSC: 37K40 35C08 35Q55 39A12 PDF BibTeX XML Cite \textit{X.-Y. Wen} et al., Rep. Math. Phys. 72, No. 3, 349--367 (2013; Zbl 1396.37076) Full Text: DOI OpenURL
Bao, Weizhu; Jian, Huaiyu; Mauser, Norbert J.; Zhang, Yong Dimension reduction of the Schrödinger equation with Coulomb and anisotropic confining potentials. (English) Zbl 1294.35130 SIAM J. Appl. Math. 73, No. 6, 2100-2123 (2013). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 65N35 65T40 65T50 81-08 PDF BibTeX XML Cite \textit{W. Bao} et al., SIAM J. Appl. Math. 73, No. 6, 2100--2123 (2013; Zbl 1294.35130) Full Text: DOI OpenURL
Bidégaray-Fesquet, Brigitte; Dumas, Eric; James, Guillaume From Newton’s cradle to the discrete \(p\)-Schrödinger equation. (English) Zbl 1292.34008 SIAM J. Math. Anal. 45, No. 6, 3404-3430 (2013). Reviewer: Li Changpin (Logan) MSC: 34A33 39A12 34E13 70F45 70K70 70K75 34C15 PDF BibTeX XML Cite \textit{B. Bidégaray-Fesquet} et al., SIAM J. Math. Anal. 45, No. 6, 3404--3430 (2013; Zbl 1292.34008) Full Text: DOI arXiv OpenURL
Cheng, Junwei; Zhang, Dajun Conservation laws of some lattice equations. (English) Zbl 1279.39005 Front. Math. China 8, No. 5, 1001-1016 (2013). MSC: 39A14 39A12 37K10 35Q55 PDF BibTeX XML Cite \textit{J. Cheng} and \textit{D. Zhang}, Front. Math. China 8, No. 5, 1001--1016 (2013; Zbl 1279.39005) Full Text: DOI arXiv OpenURL
Kevrekidis, Panayotis G.; Pelinovsky, Dmitry E.; Tyugin, Dmitry Y. Nonlinear dynamics in PT-symmetric lattices. (English) Zbl 1284.35402 J. Phys. A, Math. Theor. 46, No. 36, Article ID 365201, 17 p. (2013). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q55 82B20 78A60 PDF BibTeX XML Cite \textit{P. G. Kevrekidis} et al., J. Phys. A, Math. Theor. 46, No. 36, Article ID 365201, 17 p. (2013; Zbl 1284.35402) Full Text: DOI arXiv OpenURL
Karachalios, N. I.; Sánchez-Rey, B.; Kevrekidis, P. G.; Cuevas, J. Breathers for the discrete nonlinear Schrödinger equation with nonlinear hopping. (English) Zbl 1323.37047 J. Nonlinear Sci. 23, No. 2, 205-239 (2013); erratum ibid. 23, No. 3, 525 (2013). Reviewer: Eszter Gselmann (Debrecen) MSC: 37K60 35C07 35Q55 37K40 39A14 PDF BibTeX XML Cite \textit{N. I. Karachalios} et al., J. Nonlinear Sci. 23, No. 2, 205--239 (2013; Zbl 1323.37047) Full Text: DOI arXiv OpenURL
Achilleos, V.; Álvarez, A.; Cuevas, J.; Frantzeskakis, D. J.; Karachalios, N. I.; Kevrekidis, P. G.; Sánchez-Rey, B. Escape dynamics in the discrete repulsive \({\phi}^4\) model. (English) Zbl 1308.35260 Physica D 244, No. 1, 1-24 (2013). MSC: 35Q55 39A12 78A37 81Q05 35B32 35C08 35B35 81Q10 PDF BibTeX XML Cite \textit{V. Achilleos} et al., Physica D 244, No. 1, 1--24 (2013; Zbl 1308.35260) Full Text: DOI arXiv OpenURL
Pankov, Alexander Standing waves for discrete nonlinear Schrödinger equations: sign-changing nonlinearities. (English) Zbl 1266.37043 Appl. Anal. 92, No. 2, 308-317 (2013). Reviewer: Ahmed Hegazi (Mansoura) MSC: 37L60 39A12 39A70 47J30 PDF BibTeX XML Cite \textit{A. Pankov}, Appl. Anal. 92, No. 2, 308--317 (2013; Zbl 1266.37043) Full Text: DOI OpenURL
Sakhnovich, Alexander L.; Sakhnovich, Lev A.; Roitberg, Inna Ya. Inverse problems and nonlinear evolution equations. Solutions, Darboux matrices and Weyl-Titchmarsh functions. (English) Zbl 1283.47003 de Gruyter Studies in Mathematics 47. Berlin: De Gruyter (ISBN 978-3-11-025860-8/hbk; 978-3-11-025861-5/ebook). xiii, 341 p. (2013). Reviewer: Josef Diblík (Brno) MSC: 47-02 47N20 47A48 34L40 34B20 35G61 35Q51 37K15 37K35 35F46 35A01 35A02 35Q41 39A12 93B28 65N21 65M32 PDF BibTeX XML Cite \textit{A. L. Sakhnovich} et al., Inverse problems and nonlinear evolution equations. Solutions, Darboux matrices and Weyl-Titchmarsh functions. Berlin: De Gruyter (2013; Zbl 1283.47003) OpenURL
Zhang, Guoping Recent advances in the discrete nonlinear Schrödinger equation with unbounded potential. (English) Zbl 1298.35210 Pac. J. Appl. Math. 4, No. 2, 117-123 (2012). MSC: 35Q55 35Q51 37L60 39A12 39A70 47J30 78A40 PDF BibTeX XML Cite \textit{G. Zhang}, Pac. J. Appl. Math. 4, No. 2, 117--123 (2012; Zbl 1298.35210) OpenURL
Mizumachi, Tetsu; Pelinovsky, Dmitry On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation. (English) Zbl 1260.37047 Discrete Contin. Dyn. Syst., Ser. S 5, No. 5, 971-987 (2012). Reviewer: Jens Rademacher (Bremen) MSC: 37K60 35B35 35Q55 37K40 PDF BibTeX XML Cite \textit{T. Mizumachi} and \textit{D. Pelinovsky}, Discrete Contin. Dyn. Syst., Ser. S 5, No. 5, 971--987 (2012; Zbl 1260.37047) Full Text: DOI 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
Krüger, Helge; Teschl, Gerald Unique continuation for discrete nonlinear wave equations. (English) Zbl 1246.35118 Proc. Am. Math. Soc. 140, No. 4, 1321-1330 (2012). Reviewer: Bilender P. Allahverdiev (Isparta) MSC: 35L05 39A12 37K60 37K15 37K10 PDF BibTeX XML Cite \textit{H. Krüger} and \textit{G. Teschl}, Proc. Am. Math. Soc. 140, No. 4, 1321--1330 (2012; Zbl 1246.35118) Full Text: DOI arXiv OpenURL
Zhou, Yangfeng; Shen, Zifei Ground state solutions for a discrete Schrödinger system with superlinear nonlinearities. (Chinese. English summary) Zbl 1265.35339 J. Zhejiang Norm. Univ., Nat. Sci. 34, No. 4, 372-378 (2011). MSC: 35Q55 PDF BibTeX XML Cite \textit{Y. Zhou} and \textit{Z. Shen}, J. Zhejiang Norm. Univ., Nat. Sci. 34, No. 4, 372--378 (2011; Zbl 1265.35339) OpenURL
Ezzoug, Emna; Kechiche, Wided; Zahrouni, Ezzeddine Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect. (English) Zbl 1229.65169 Appl. Math. Comput. 217, No. 19, 7818-7830 (2011). Reviewer: Snezhana Gocheva-Ilieva (Plovdiv) MSC: 65M20 65M06 35Q55 37D45 37K10 PDF BibTeX XML Cite \textit{E. Ezzoug} et al., Appl. Math. Comput. 217, No. 19, 7818--7830 (2011; Zbl 1229.65169) Full Text: DOI OpenURL