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Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation

Nikos I. Karachalios·Athanasios N. Yannacopoulos
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Abstract

We study the asymptotic behavior of solutions of discrete nonlinear Schrödinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions. Similarities and differences with the continuous counterpart (NLS-partial differential equation) are pointed out. For a dissipative system we prove existence of a global attractor and its stability under finite dimensional approximations. Similar questions are treated in a weighted phase space. Finally, we propose possible extensions for various types of DNLS equations.

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Nikos I. Karachalios, Athanasios N. Yannacopoulos. 2005-03-15. Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation. https://arxiv.org/abs/math/0503298

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