Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501569 | Journal of Differential Equations | 2005 | 36 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Nikos I. Karachalios, Athanasios N. Yannacopoulos,