We study the dynamics of two coupled perturbed discretized NLS equations with periodic boundary conditions. The unperturbed system consists of two integrable discrete NLS equations, for which the corresponding Lax pairs are known. We describe here the homoclinic orbits of the coupled system and give new results for a class of non-integrable perturbations through a Mel'nikov type approach, using the spectral analysis of Lax's operators and Fenichel's theory.
- Coupled discrete Nonlinear Schrödinger equations
- Mel'nikov theory
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics