On localized solutions of discrete nonlinear Schrodinger equation. An exact result

Abstract

Local and global existence of localized solutions of a discrete nonlinear Schrodinger (DNLS) equation, with arbitrary on-site nonlinearity, is proved. In particular, it is shown that an initially localized excitation persists localized during infinite time. Moreover, if initial localization is stronger than |n|^{-d} with any power d, it maintains itself as such during infinite time. The results are generalized to various types of inter-side and saturable nonlinearities, to lattices with long range interactions, as well as DNLS with dissipation.

arXiv comment15 pages, accepted for publication in Physica D

References in corpus (1)

• On classification of intrinsic localized modes for the Discrete Nonlinear Schrödinger Equation

Cited by in corpus (3)

• Heteroclinic standing waves in defocussing DNLS equations -- Variational approach via energy minimization
• The closeness of localised structures between the Ablowitz-Ladik lattice and Discrete Nonlinear Schrödinger equations II: Generalised AL and DNLS systems
• Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schrödinger equation: justification and numerical comparisons