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Applicable Analysis
An International Journal
Volume 85, 2006 - Issue 12
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Original Articles

Dispersive estimates for 1D discrete Schrödinger and Klein–Gordon equations

A. I. Komech Faculty of Mathematics, Vienna University, A-1090 Vienna, AustriaCorrespondence[email protected]
,
E. A. Kopylova Wolfgang pauli Institute, Vienna University, A-1090 Vienna, Austria
&
M. Kunze Universität Duisburg-Essen, Fachbereich Mathematick, D-45117 Essen, Germany
Pages 1487-1508 | Received 13 Jun 2005, Published online: 11 Dec 2006

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Masaya Maeda. (2021) Stabilization of small solutions of discrete NLS with potential having two eigenvalues. Applicable Analysis 100:8, pages 1603-1633.
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E.A. Kopylova. (2010) On asymptotic stability of solitary waves in discrete Klein–Gordon equation coupled to a nonlinear oscillator. Applicable Analysis 89:9, pages 1467-1492.
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Articles from other publishers (33)

Masaya Maeda. (2022) Asymptotic stability of small bound state of nonlinear quantum walks. Physica D: Nonlinear Phenomena 439, pages 133408.
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Dirk Hennig & Nikos I. Karachalios. (2021) Existence of exponentially spatially localized breather solutions for lattices of nonlinearly coupled particles: Schauder’s fixed point theorem approach. Journal of Mathematical Physics 62:12.
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Alexander Komech & Elena Kopylova. 2021. Attractors of Hamiltonian Nonlinear Partial Differential Equations. Attractors of Hamiltonian Nonlinear Partial Differential Equations.
Dirk Hennig. (2021) Localised time-periodic solutions of discrete nonlinear Klein–Gordon systems with convex on-site potentials. Journal of Fixed Point Theory and Applications 23:2.
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Dario Bambusi & Zhiyan Zhao. (2020) Dispersive estimate for quasi-periodic Schrödinger operators on 1-d lattices. Advances in Mathematics 366, pages 107071.
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Yue Mi & Zhiyan Zhao. (2020) Dispersive estimate for two-periodic discrete one-dimensional Schrödinger operator. Journal of Mathematical Analysis and Applications 485:1, pages 123768.
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Татьяна Владимировна Дудникова & Tatiana Vladimirovna Dudnikova. (2020) Стабилизация статистических решений для бесконечной неоднородной цепочки гармонических осцилляторовStabilization of Statistical Solutions for an Infinite Inhomogeneous Chain of Harmonic OscillatorsДифференциальные уравнения и динамические системыDifferential equations and dynamical systems. Труды Математического института имени В.А. Стеклова Trudy Matematicheskogo Instituta imeni V.A. Steklova 308, pages 181-196.
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A. I. Komech & E. A. Kopylova. (2020) Attractors of nonlinear Hamiltonian partial differential equations. Russian Mathematical Surveys 75:1, pages 1-87.
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Александр Ильич Комеч, Aleksandr Il'ich KomechЕлена Андреевна Копылова & Elena Andreevna Kopylova. (2020) Аттракторы нелинейных гамильтоновых уравнений в частных производныхAttractors of nonlinear Hamiltonian partial differential equations. Успехи математических наук Uspekhi Matematicheskikh Nauk 75:1(451), pages 3-94.
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T. V. Dudnikova. (2020) Stabilization of Statistical Solutions for an Infinite Inhomogeneous Chain of Harmonic Oscillators. Proceedings of the Steklov Institute of Mathematics 308:1, pages 168-183.
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T.V. Dudnikova. (2018) Behavior for Large Time of a Two-Component Chain of Harmonic Oscillators. Russian Journal of Mathematical Physics 25:4, pages 470-491.
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T. V. Dudnikova. (2018) Large-Time Behavior of an Infinite System of Harmonic Oscillators on the Half-Line. Proceedings of the Steklov Institute of Mathematics 301:1, pages 82-97.
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Tatiana Vladimirovna Dudnikova. (2018) Infinite non homogeneous chain of harmonic oscillators: Stabilization of statistical solutions. Keldysh Institute Preprints:254, pages 1-24.
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T. V. Dudnikova. (2017) On convergence to equilibrium for one-dimensional chain of harmonic oscillators on the half-line. Journal of Mathematical Physics 58:4.
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T. V. Dudnikova. (2016) Long-Time Asymptotics of Solutions to a Hamiltonian System on a Lattice. Journal of Mathematical Sciences 219:1, pages 69-85.
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Alexander Komech. (2016) Attractors of Hamilton nonlinear PDEs. Discrete and Continuous Dynamical Systems 36:11, pages 6201-6256.
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August J. Krueger & Avy Soffer. (2015) Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates. Annales Henri Poincaré 17:5, pages 1181-1208.
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Elena Kopylova & Gerald Teschl. (2016) Dispersion estimates for one-dimensional discrete Dirac equations. Journal of Mathematical Analysis and Applications 434:1, pages 191-208.
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August J. Krueger & Avy Soffer. (2015) Structure of Noncommutative Solitons: Existence and Spectral Theory. Letters in Mathematical Physics 105:10, pages 1377-1398.
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E. Kopylova. (2015) Limiting absorption principle for the 1D discrete Dirac equation. Russian Journal of Mathematical Physics 22:1, pages 34-38.
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Dario Bambusi. (2013) Asymptotic Stability of Breathers in Some Hamiltonian Networks of Weakly Coupled Oscillators. Communications in Mathematical Physics 324:2, pages 515-547.
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Alexander Komech & Elena Kopylova. 2012. Dispersion Decay and Scattering Theory. Dispersion Decay and Scattering Theory 167 172 .
Tetsu Mizumachi & Dmitry Pelinovsky. (2012) On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - S 5:5, pages 971-987.
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K. Kirkpatrick. (2012) Solitons and Gibbs Measures for Nonlinear Schrödinger Equations. Mathematical Modelling of Natural Phenomena 7:2, pages 95-112.
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Liviu I. Ignat & Diana Stan. (2011) Dispersive Properties for Discrete Schrödinger Equations. Journal of Fourier Analysis and Applications 17:5, pages 1035-1065.
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Dmitry Pelinovsky & Anton Sakovich. (2011) Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation. Physica D: Nonlinear Phenomena 240:3, pages 265-281.
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I. A. Ado. (2010) Scattering problem in a quantum waveguide in a tight-binding model. Moscow University Physics Bulletin 65:5, pages 345-350.
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E.A. Kopylova & A.I. Komech. (2010) Long time decay for 2D Klein–Gordon equation. Journal of Functional Analysis 259:2, pages 477-502.
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P. G. Kevrekidis, D. E. Pelinovsky & A. Stefanov. (2009) Asymptotic Stability of Small Bound States in the Discrete Nonlinear Schrödinger Equation. SIAM Journal on Mathematical Analysis 41:5, pages 2010-2030.
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Panayotis G. KevrekidisAtanas Stefanov. 2009. The Discrete Nonlinear Schrödinger Equation. The Discrete Nonlinear Schrödinger Equation 401 412 .
E. A. Kopylova. (2008) Existence of solitary waves for the discrete Schrödinger equation coupled to a nonlinear oscillator. Russian Journal of Mathematical Physics 15:4, pages 487-492.
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D. E. Pelinovsky & A. Stefanov. (2008) On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension. Journal of Mathematical Physics 49:11.
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A.I. Komech, E.A. Kopylova & B.R. Vainberg. (2008) On dispersive properties of discrete 2D Schrödinger and Klein–Gordon equations. Journal of Functional Analysis 254:8, pages 2227-2254.
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