Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation

Details Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation

2005-03-15

arxiv.org/abs/math/0503298v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We study the asymptotic behavior of solutions of discrete nonlinear Schr\"odinger-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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