Global existence and compact attractors for the discrete nonlinear Schrödinger equation
By Nikos I. Karachalios, Athanasios N. Yannacopoulos. 2005
90 citations recorded by the source corpus.
Abstract We study the asymptotic behavior of solutions of discrete nonlinear Schrodinger-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.
Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1401059bd0fc44e052e5cbb1c06da6c008656db4
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In Control and Systems Engineering
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, background): “, ε = 0), traveling waves of lattice systems have been investigated in [1, 4, 5, 20, 30, 31, 32, 62], the chaotic properties of solutions have been studied in [19, 21, 22], and global attractors have been explored in [6, 10, 43, 49, 60].”
- Invariant measures of stochastic delay lattice systems (2021, background): “The solutions and their long-term dynamics of deterministic lattice systems have been studied in [1, 2, 3, 17, 24, 25, 26, 34, 67] and [4, 8, 16, 18, 19, 39, 52, 60], respectively.”
- Asymptotic behavior of non-autonomous lattice systems (2007, background): “For the asymptotic behavior of lattice systems, we refer the reader to [6,18,26,28].”