On localized solutions of discrete nonlinear Schrodinger equation. An exact result
Pattern Formation and Solitons
2009-11-11 v1 Disordered Systems and Neural Networks
Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.nlin/0504039,
title = {On localized solutions of discrete nonlinear Schrodinger equation. An exact result},
author = {P. Pacciani and V. V. Konotop and G. Perla Menzala},
journal= {arXiv preprint arXiv:nlin/0504039},
year = {2009}
}
Comments
15 pages, accepted for publication in Physica D