Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation

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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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Classical Analysis and ODEs, Dynamical Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/74501

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503298
 http://arxiv.org/abs/math/0503298

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arXiv