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
Hennig, Dirk; Karachalios, Nikos I.; Cuevas-Maraver, Jesús The closeness of the Ablowitz-Ladik lattice to the discrete nonlinear Schrödinger equation. (English) Zbl 07486719 J. Differ. Equations 316, 346-363 (2022). MSC: 35Qxx 39Axx 78Axx PDF BibTeX XML Cite \textit{D. Hennig} et al., J. Differ. Equations 316, 346--363 (2022; Zbl 07486719) Full Text: DOI arXiv OpenURL
Hennig, Dirk; Karachalios, Nikos I. Existence of exponentially spatially localized breather solutions for lattices of nonlinearly coupled particles: Schauder’s fixed point theorem approach. (English) Zbl 1493.37088 J. Math. Phys. 62, No. 12, 123506, 12 p. (2021). Reviewer: Luen-Chau Li (University Park) MSC: 37K60 47H10 47N20 PDF BibTeX XML Cite \textit{D. Hennig} and \textit{N. I. Karachalios}, J. Math. Phys. 62, No. 12, 123506, 12 p. (2021; Zbl 1493.37088) 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
Baldovin, Marco; Iubini, Stefano; Livi, Roberto; Vulpiani, Angelo Statistical mechanics of systems with negative temperature. (English) Zbl 07405118 Phys. Rep. 923, 1-50 (2021). MSC: 81-XX 82-XX PDF BibTeX XML Cite \textit{M. Baldovin} et al., Phys. Rep. 923, 1--50 (2021; Zbl 07405118) Full Text: DOI arXiv OpenURL
Hennig, Dirk Localised time-periodic solutions of discrete nonlinear Klein-Gordon systems with convex on-site potentials. (English) Zbl 1476.34049 J. Fixed Point Theory Appl. 23, No. 2, Paper No. 31, 8 p. (2021). MSC: 34A33 34C25 34C15 47H10 PDF BibTeX XML Cite \textit{D. Hennig}, J. Fixed Point Theory Appl. 23, No. 2, Paper No. 31, 8 p. (2021; Zbl 1476.34049) Full Text: DOI arXiv OpenURL
Diamantidis, Sevastos; Horikis, Theodoros P.; Karachalios, Nikos I. Exciting extreme events in the damped and AC-driven NLS equation through plane-wave initial conditions. (English) Zbl 1462.35352 Chaos 31, No. 5, 053103, 20 p. (2021). MSC: 35Q55 PDF BibTeX XML Cite \textit{S. Diamantidis} et al., Chaos 31, No. 5, 053103, 20 p. (2021; Zbl 1462.35352) Full Text: DOI arXiv OpenURL
Herrmann, Michael; Matthies, Karsten A uniqueness result for a simple superlinear eigenvalue problem. (English) Zbl 1467.45001 J. Nonlinear Sci. 31, No. 2, Paper No. 27, 29 p. (2021). MSC: 45C05 45G10 45M05 47J10 PDF BibTeX XML Cite \textit{M. Herrmann} and \textit{K. Matthies}, J. Nonlinear Sci. 31, No. 2, Paper No. 27, 29 p. (2021; Zbl 1467.45001) Full Text: DOI arXiv 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
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
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
Herrmann, Michael; Matthies, Karsten Nonlinear and nonlocal eigenvalue problems: variational existence, decay properties, approximation, and universal scaling limits. (English) Zbl 07225377 Nonlinearity 33, No. 8, 4046-4074 (2020). MSC: 47J10 45G10 45M05 45C05 49R05 PDF BibTeX XML Cite \textit{M. Herrmann} and \textit{K. Matthies}, Nonlinearity 33, No. 8, 4046--4074 (2020; Zbl 07225377) Full Text: DOI OpenURL
Martínez-Galicia, Ricardo; Panayotaros, Panayotis Classical breathers and quantum coherent states in discrete NLS systems. (English) Zbl 1428.81027 Phys. Lett., A 383, No. 2-3, 164-169 (2019). MSC: 81P40 35Q55 PDF BibTeX XML Cite \textit{R. Martínez-Galicia} and \textit{P. Panayotaros}, Phys. Lett., A 383, No. 2--3, 164--169 (2019; Zbl 1428.81027) Full Text: DOI OpenURL
Cuevas-Maraver, J.; Kevrekidis, P. G.; Malomed, Boris A.; Guo, Lijuan Solitary waves in the Ablowitz-Ladik equation with power-law nonlinearity. (English) Zbl 1425.35178 J. Phys. A, Math. Theor. 52, No. 6, Article ID 065202, 14 p. (2019). MSC: 35Q55 35C08 35J87 35B35 PDF BibTeX XML Cite \textit{J. Cuevas-Maraver} et al., J. Phys. A, Math. Theor. 52, No. 6, Article ID 065202, 14 p. (2019; Zbl 1425.35178) Full Text: DOI arXiv OpenURL
Herrmann, Michael; Matthies, Karsten Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains. (English) Zbl 1428.37070 Trans. Am. Math. Soc. 372, No. 5, 3425-3486 (2019). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 37K60 37K40 70H14 74H10 PDF BibTeX XML Cite \textit{M. Herrmann} and \textit{K. Matthies}, Trans. Am. Math. Soc. 372, No. 5, 3425--3486 (2019; Zbl 1428.37070) Full Text: DOI arXiv OpenURL
Adami, Riccardo; Dovetta, Simone; Serra, Enrico; Tilli, Paolo Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs. (English) Zbl 1414.35202 Anal. PDE 12, No. 6, 1597-1612 (2019). MSC: 35Q55 35R02 PDF BibTeX XML Cite \textit{R. Adami} et al., Anal. PDE 12, No. 6, 1597--1612 (2019; Zbl 1414.35202) Full Text: DOI arXiv OpenURL
Chen, Sitong; Tang, Xianhua; Yu, Jianshe Sign-changing ground state solutions for discrete nonlinear Schrödinger equations. (English) Zbl 1411.39006 J. Difference Equ. Appl. 25, No. 2, 202-218 (2019). MSC: 39A12 39A70 PDF BibTeX XML Cite \textit{S. Chen} et al., J. Difference Equ. Appl. 25, No. 2, 202--218 (2019; Zbl 1411.39006) Full Text: DOI OpenURL
Xie, Qilin Multiple solutions for the nonhomogeneous discrete nonlinear Schrödinger equation. (English) Zbl 1409.39003 Appl. Math. Lett. 91, 144-150 (2019). MSC: 39A10 39A22 35Q55 PDF BibTeX XML Cite \textit{Q. Xie}, Appl. Math. Lett. 91, 144--150 (2019; Zbl 1409.39003) Full Text: DOI OpenURL
Rusin, Rahmi; Kusdiantara, Rudy; Susanto, Hadi Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schrödinger lattices. (English) Zbl 1411.35243 J. Phys. A, Math. Theor. 51, No. 47, Article ID 475202, 13 p. (2018). MSC: 35Q55 39A12 35C08 35A15 28C20 PDF BibTeX XML Cite \textit{R. Rusin} et al., J. Phys. A, Math. Theor. 51, No. 47, Article ID 475202, 13 p. (2018; Zbl 1411.35243) Full Text: DOI arXiv OpenURL
Zhang, Luyu; Ma, Shiwang Ground state solutions for periodic discrete nonlinear Schrödinger equations with saturable nonlinearities. (English) Zbl 1446.39011 Adv. Difference Equ. 2018, Paper No. 176, 13 p. (2018). MSC: 39A14 35Q55 39A12 39A70 PDF BibTeX XML Cite \textit{L. Zhang} and \textit{S. Ma}, Adv. Difference Equ. 2018, Paper No. 176, 13 p. (2018; Zbl 1446.39011) Full Text: DOI OpenURL
Choi, Mi-Ran; Hundertmark, Dirk; Lee, Young-Ran Discrete diffraction managed solitons: threshold phenomena and rapid decay for general nonlinearities. (English) Zbl 1374.78027 J. Math. Phys. 58, No. 10, 101513, 43 p. (2017). MSC: 78A45 78A60 35Q55 39A12 49J20 35C08 PDF BibTeX XML Cite \textit{M.-R. Choi} et al., J. Math. Phys. 58, No. 10, 101513, 43 p. (2017; Zbl 1374.78027) Full Text: DOI arXiv Link OpenURL
Choi, Mi-Ran; Hundertmark, Dirk; Lee, Young-Ran Thresholds for existence of dispersion management solitons for general nonlinearities. (English) Zbl 1432.35184 SIAM J. Math. Anal. 49, No. 2, 1519-1569 (2017). MSC: 35Q51 35C08 35Q55 35Q60 49J10 78A60 PDF BibTeX XML Cite \textit{M.-R. Choi} et al., SIAM J. Math. Anal. 49, No. 2, 1519--1569 (2017; Zbl 1432.35184) 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
D’Aguì, Giuseppina; Mawhin, Jean; Sciammetta, Angela Positive solutions for a discrete two point nonlinear boundary value problem with \(p\)-Laplacian. (English) Zbl 1352.39002 J. Math. Anal. Appl. 447, No. 1, 383-397 (2017). MSC: 39A12 39A22 34B15 PDF BibTeX XML Cite \textit{G. D'Aguì} et al., J. Math. Anal. Appl. 447, No. 1, 383--397 (2017; Zbl 1352.39002) Full Text: DOI OpenURL
Stockhofe, J.; Schmelcher, P. Modulational instability and localized breather modes in the discrete nonlinear Schrödinger equation with helicoidal hopping. (English) Zbl 1368.35252 Physica D 328-329, 9-20 (2016). MSC: 35Q55 35C08 35B35 PDF BibTeX XML Cite \textit{J. Stockhofe} and \textit{P. Schmelcher}, Physica D 328--329, 9--20 (2016; Zbl 1368.35252) Full Text: DOI arXiv OpenURL
Paleari, Simone; Penati, Tiziano Long time stability of small-amplitude breathers in a mixed FPU-KG model. (English) Zbl 1368.37071 Z. Angew. Math. Phys. 67, No. 6, Article ID 148, 21 p. (2016). MSC: 37J45 70H14 70K45 35Q55 PDF BibTeX XML Cite \textit{S. Paleari} and \textit{T. Penati}, Z. Angew. Math. Phys. 67, No. 6, Article ID 148, 21 p. (2016; Zbl 1368.37071) Full Text: DOI arXiv 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
Chen, Guanwei; Schechter, Martin Non-periodic discrete Schrödinger equations: ground state solutions. (English) Zbl 1375.39011 Z. Angew. Math. Phys. 67, No. 3, Article ID 72, 15 p. (2016). Reviewer: Ioannis P. Stavroulakis (Ioannina) MSC: 39A12 35Q51 35Q55 PDF BibTeX XML Cite \textit{G. Chen} and \textit{M. Schechter}, Z. Angew. Math. Phys. 67, No. 3, Article ID 72, 15 p. (2016; Zbl 1375.39011) Full Text: DOI OpenURL
Tang, Xian Hua Non-Nehari manifold method for periodic discrete superlinear Schrödinger equation. (English) Zbl 1386.39015 Acta Math. Sin., Engl. Ser. 32, No. 4, 463-473 (2016). MSC: 39A12 58E05 70H05 PDF BibTeX XML Cite \textit{X. H. Tang}, Acta Math. Sin., Engl. Ser. 32, No. 4, 463--473 (2016; Zbl 1386.39015) 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
Ben, Roberto I.; Cisneros Ake, Luís; Minzoni, A. A.; Panayotaros, Panayotis Localized solutions for a nonlocal discrete NLS equation. (English) Zbl 1343.35210 Phys. Lett., A 379, No. 30-31, 1705-1714 (2015). MSC: 35Q55 39A14 81Q37 82D30 PDF BibTeX XML Cite \textit{R. I. Ben} et al., Phys. Lett., A 379, No. 30--31, 1705--1714 (2015; Zbl 1343.35210) Full Text: DOI OpenURL
Bonanno, Claudio A complexity approach to the soliton resolution conjecture. (English) Zbl 1327.35332 J. Stat. Phys. 160, No. 5, 1432-1448 (2015). MSC: 35Q51 68Q30 35Q55 PDF BibTeX XML Cite \textit{C. Bonanno}, J. Stat. Phys. 160, No. 5, 1432--1448 (2015; Zbl 1327.35332) Full Text: DOI arXiv OpenURL
Cheng, Ming Solitary waves of the Schrödinger lattice system with nonlinear hopping. (English) Zbl 1330.35396 J. Funct. Spaces 2015, Article ID 385649, 7 p. (2015). MSC: 35Q55 35R20 35B10 35C08 PDF BibTeX XML Cite \textit{M. Cheng}, J. Funct. Spaces 2015, Article ID 385649, 7 p. (2015; Zbl 1330.35396) Full Text: DOI arXiv OpenURL
Sun, Jijiang; Ma, Shiwang Multiple solutions for discrete periodic nonlinear Schrödinger equations. (English) Zbl 1360.81152 J. Math. Phys. 56, No. 2, 022110, 16 p. (2015). MSC: 81Q05 81Q10 35Q55 39A12 PDF BibTeX XML Cite \textit{J. Sun} and \textit{S. Ma}, J. Math. Phys. 56, No. 2, 022110, 16 p. (2015; Zbl 1360.81152) Full Text: DOI OpenURL
Chatterjee, Sourav Invariant measures and the soliton resolution conjecture. (English) Zbl 1303.35096 Commun. Pure Appl. Math. 67, No. 11, 1737-1842 (2014). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35C08 PDF BibTeX XML Cite \textit{S. Chatterjee}, Commun. Pure Appl. Math. 67, No. 11, 1737--1842 (2014; Zbl 1303.35096) Full Text: DOI arXiv OpenURL
Fukuizumi, Reika; Sacchetti, Andrea Stationary states for nonlinear Schrödinger equations with periodic potentials. (English) Zbl 1302.35347 J. Stat. Phys. 156, No. 4, 707-738 (2014). MSC: 35Q55 81Q20 PDF BibTeX XML Cite \textit{R. Fukuizumi} and \textit{A. Sacchetti}, J. Stat. Phys. 156, No. 4, 707--738 (2014; Zbl 1302.35347) Full Text: DOI OpenURL
Panayotaros, Panayotis; Marchant, T. R. Solitary waves in nematic liquid crystals. (English) Zbl 1291.35360 Physica D 268, 106-117 (2014). MSC: 35Q55 35Q51 78A60 76A15 35B65 35B35 PDF BibTeX XML Cite \textit{P. Panayotaros} and \textit{T. R. Marchant}, Physica D 268, 106--117 (2014; Zbl 1291.35360) Full Text: DOI Link OpenURL
Sun, Guowei On standing wave solutions for discrete nonlinear Schrödinger equations. (English) Zbl 1295.39004 Abstr. Appl. Anal. 2013, Article ID 436919, 6 p. (2013). MSC: 39A12 35Q55 PDF BibTeX XML Cite \textit{G. Sun}, Abstr. Appl. Anal. 2013, Article ID 436919, 6 p. (2013; Zbl 1295.39004) Full Text: DOI 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
Chen, Wen-xiong; Yang, Min-bo Standing waves for periodic discrete nonlinear Schrödinger equations with asymptotically linear terms. (English) Zbl 1359.35175 Acta Math. Appl. Sin., Engl. Ser. 28, No. 2, 351-360 (2012). MSC: 35Q55 35Q51 39A12 39A70 35B38 PDF BibTeX XML Cite \textit{W.-x. Chen} and \textit{M.-b. Yang}, Acta Math. Appl. Sin., Engl. Ser. 28, No. 2, 351--360 (2012; Zbl 1359.35175) Full Text: DOI OpenURL
Hundertmark, Dirk; Lee, Young-Ran On non-local variational problems with lack of compactness related to non-linear optics. (English) Zbl 1244.49008 J. Nonlinear Sci. 22, No. 1, 1-38 (2012). MSC: 49J20 35Q93 78A10 PDF BibTeX XML Cite \textit{D. Hundertmark} and \textit{Y.-R. Lee}, J. Nonlinear Sci. 22, No. 1, 1--38 (2012; Zbl 1244.49008) Full Text: DOI arXiv OpenURL
Chen, Guanwei; Ma, Shiwang Discrete nonlinear Schrödinger equations with superlinear nonlinearities. (English) Zbl 1254.39006 Appl. Math. Comput. 218, No. 9, 5496-5507 (2012). Reviewer: Bilender P. Allahverdiev (Isparta) MSC: 39A12 39A10 39A70 PDF BibTeX XML Cite \textit{G. Chen} and \textit{S. Ma}, Appl. Math. Comput. 218, No. 9, 5496--5507 (2012; Zbl 1254.39006) Full Text: DOI 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
Zhang, Guoping Breather solutions of the discrete nonlinear Schrödinger equations with sign changing nonlinearity. (English) Zbl 1316.35270 J. Math. Phys. 52, No. 4, 043516, 11 p. (2011). MSC: 35Q55 39A12 35C08 PDF BibTeX XML Cite \textit{G. Zhang}, J. Math. Phys. 52, No. 4, 043516, 11 p. (2011; Zbl 1316.35270) Full Text: DOI OpenURL
Cheng, Ming Excitation threshold for the discrete coupled Schrödinger lattice system. (English) Zbl 1314.35160 J. Math. Phys. 52, No. 2, 023508, 11 p. (2011). MSC: 35Q55 39A12 82D25 37K60 PDF BibTeX XML Cite \textit{M. Cheng}, J. Math. Phys. 52, No. 2, 023508, 11 p. (2011; Zbl 1314.35160) Full Text: DOI OpenURL
Achilleos, V.; Theocharis, G.; Kevrekidis, P. G.; Karachalios, N. I.; Diakonos, F. K.; Frantzeskakis, D. J. Stationary states of a nonlinear Schrödinger lattice with a harmonic trap. (English) Zbl 1272.35172 J. Math. Phys. 52, No. 9, 092701, 25 p. (2011). MSC: 35Q55 39A12 78A37 81Q05 35B32 35C08 35B35 81Q10 PDF BibTeX XML Cite \textit{V. Achilleos} et al., J. Math. Phys. 52, No. 9, 092701, 25 p. (2011; Zbl 1272.35172) Full Text: DOI arXiv Link OpenURL
Yang, Minbo Standing waves to discrete vector nonlinear Schrödinger equation. (English) Zbl 1244.35139 J. Difference Equ. Appl. 17, No. 10, 1455-1469 (2011). Reviewer: M. Marin (Brasov) MSC: 35Q55 39A12 35B38 PDF BibTeX XML Cite \textit{M. Yang}, J. Difference Equ. Appl. 17, No. 10, 1455--1469 (2011; Zbl 1244.35139) Full Text: DOI OpenURL
Zhang, Guoping; Pankov, Alexander Standing wave solutions of the discrete non-linear Schrödinger equations with unbounded potentials. II. (English) Zbl 1387.35558 Appl. Anal. 89, No. 9, 1541-1557 (2010). MSC: 35Q55 35Q51 47J30 34A33 37L60 39A12 58E05 78A40 PDF BibTeX XML Cite \textit{G. Zhang} and \textit{A. Pankov}, Appl. Anal. 89, No. 9, 1541--1557 (2010; Zbl 1387.35558) Full Text: DOI OpenURL
Cuevas, J.; Karachalios, N. I.; Palmero, F. Energy thresholds for the existence of breather solutions and travelling waves on lattices. (English) Zbl 1193.37104 Appl. Anal. 89, No. 9, 1351-1385 (2010). MSC: 37L60 35Q55 47J30 PDF BibTeX XML Cite \textit{J. Cuevas} et al., Appl. Anal. 89, No. 9, 1351--1385 (2010; Zbl 1193.37104) Full Text: DOI Link OpenURL
Bambusi, Dario; Paleari, Simone; Penati, Tiziano Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein-Gordon lattices. (English) Zbl 1203.37121 Appl. Anal. 89, No. 9, 1313-1334 (2010). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37K50 34C25 65N30 37K60 PDF BibTeX XML Cite \textit{D. Bambusi} et al., Appl. Anal. 89, No. 9, 1313--1334 (2010; Zbl 1203.37121) Full Text: DOI arXiv OpenURL
Shi, Haiping Gap solitons in periodic discrete Schrödinger equations with nonlinearity. (English) Zbl 1190.35192 Acta Appl. Math. 109, No. 3, 1065-1075 (2010). MSC: 35Q51 35Q55 39A70 35A15 PDF BibTeX XML Cite \textit{H. Shi}, Acta Appl. Math. 109, No. 3, 1065--1075 (2010; Zbl 1190.35192) Full Text: DOI OpenURL
Yang, Minbo; Chen, Wenxiong; Ding, Yanheng Solutions for discrete periodic Schrödinger equations with spectrum 0. (English) Zbl 1191.35260 Acta Appl. Math. 110, No. 3, 1475-1488 (2010). MSC: 35Q55 35Q51 39A12 39A70 PDF BibTeX XML Cite \textit{M. Yang} et al., Acta Appl. Math. 110, No. 3, 1475--1488 (2010; Zbl 1191.35260) Full Text: DOI OpenURL
Yang, Minbo; Zhao, Fukun; Ding, Yanheng Infinitely many stationary solutions of discrete vector nonlinear Schrödinger equation with symmetry. (English) Zbl 1191.39011 Appl. Math. Comput. 215, No. 12, 4230-4238 (2010). Reviewer: Haydar Akca (Al Ain) MSC: 39A12 35Q55 PDF BibTeX XML Cite \textit{M. Yang} et al., Appl. Math. Comput. 215, No. 12, 4230--4238 (2010; Zbl 1191.39011) Full Text: DOI OpenURL
Zhang, Guoping; Liu, Fengshan Existence of breather solutions of the DNLS equations with unbounded potentials. (English) Zbl 1238.37030 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e786-e792 (2009). MSC: 37L60 34A33 58E05 34A35 35Q55 47J30 PDF BibTeX XML Cite \textit{G. Zhang} and \textit{F. Liu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e786--e792 (2009; Zbl 1238.37030) Full Text: DOI OpenURL
Cuevas, J.; Karachalios, N. I.; Palmero, F. Lower and upper estimates on the excitation threshold for breathers in discrete nonlinear Schrödinger lattices. (English) Zbl 1304.34022 J. Math. Phys. 50, No. 11, 112705, 10 p. (2009). MSC: 34A33 34C25 37K40 37K60 82C20 PDF BibTeX XML Cite \textit{J. Cuevas} et al., J. Math. Phys. 50, No. 11, 112705, 10 p. (2009; Zbl 1304.34022) Full Text: DOI arXiv OpenURL
Zhang, Guoping Breather solutions of the discrete nonlinear Schrödinger equations with unbounded potentials. (English) Zbl 1200.37072 J. Math. Phys. 50, No. 1, 013505, 12 p. (2009). MSC: 37K60 37K40 PDF BibTeX XML Cite \textit{G. Zhang}, J. Math. Phys. 50, No. 1, 013505, 12 p. (2009; Zbl 1200.37072) Full Text: DOI OpenURL
James, Guillaume; Sánchez-Rey, Bernardo; Cuevas, Jesús Breathers in inhomogeneous nonlinear lattices: an analysis via center manifold reduction. (English) Zbl 1178.37114 Rev. Math. Phys. 21, No. 1, 1-59 (2009). Reviewer: Victor Sharapov (Volgograd) MSC: 37L60 37K50 37K60 34C25 34C37 PDF BibTeX XML Cite \textit{G. James} et al., Rev. Math. Phys. 21, No. 1, 1--59 (2009; Zbl 1178.37114) Full Text: DOI arXiv OpenURL
Pelinovsky, D. E.; Stefanov, A. On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension. (English) Zbl 1159.81336 J. Math. Phys. 49, No. 11, 113501, 17 p. (2008). MSC: 81Q05 81Q10 39A12 47B39 47N50 PDF BibTeX XML Cite \textit{D. E. Pelinovsky} and \textit{A. Stefanov}, J. Math. Phys. 49, No. 11, 113501, 17 p. (2008; Zbl 1159.81336) Full Text: DOI arXiv Link OpenURL
Panayotaros, Panayotis Invariant tori in the discrete NLS with small amplitude diffraction management. (English) Zbl 1161.37050 Physica D 237, No. 6, 829-839 (2008). Reviewer: Hu Chuangan (Tianjin) MSC: 37K55 35Q55 PDF BibTeX XML Cite \textit{P. Panayotaros}, Physica D 237, No. 6, 829--839 (2008; Zbl 1161.37050) Full Text: DOI OpenURL
Fibich, G.; Sivan, Y.; Weinstein, M. I. Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure. (English) Zbl 1099.35130 Physica D 217, No. 1, 31-57 (2006). MSC: 35Q55 82B10 78A60 PDF BibTeX XML Cite \textit{G. Fibich} et al., Physica D 217, No. 1, 31--57 (2006; Zbl 1099.35130) Full Text: DOI OpenURL
Pelinovsky, D. E.; Kevrekidis, P. G.; Frantzeskakis, D. J. Stability of discrete solitons in nonlinear Schrödinger lattices. (English) Zbl 1088.39004 Physica D 212, No. 1-2, 1-19 (2005). Reviewer: Miloš Čanak (Beograd) MSC: 39A11 39A12 37K60 35Q51 35Q55 37K40 PDF BibTeX XML Cite \textit{D. E. Pelinovsky} et al., Physica D 212, No. 1--2, 1--19 (2005; Zbl 1088.39004) Full Text: DOI OpenURL
Karachalios, Nikos I.; Yannacopoulos, Athanasios N. Global existence and compact attractors for the discrete nonlinear Schrödinger equation. (English) Zbl 1084.35092 J. Differ. Equations 217, No. 1, 88-123 (2005). MSC: 35Q55 37L60 35B41 78A60 92D20 PDF BibTeX XML Cite \textit{N. I. Karachalios} and \textit{A. N. Yannacopoulos}, J. Differ. Equations 217, No. 1, 88--123 (2005; Zbl 1084.35092) Full Text: DOI arXiv OpenURL
Panayotaros, Panayotis Breather solutions in the diffraction managed NLS equation. (English) Zbl 1075.35079 Physica D 206, No. 3-4, 213-231 (2005). MSC: 35Q55 37K60 35A15 PDF BibTeX XML Cite \textit{P. Panayotaros}, Physica D 206, No. 3--4, 213--231 (2005; Zbl 1075.35079) Full Text: DOI OpenURL
Biship, A. R.; Kalosakas, G.; Rasmussen, K. Ø.; Kevrekidis, P. G. Localization in physical systems described by discrete nonlinear Schrödinger-type equations. (English) Zbl 1080.81075 Chaos 13, No. 2, 588-595 (2003). MSC: 81V80 78A60 82B10 PDF BibTeX XML Cite \textit{A. R. Biship} et al., Chaos 13, No. 2, 588--595 (2003; Zbl 1080.81075) Full Text: DOI OpenURL