Periodic travelling wave solutions of discrete nonlinear Schr\"odinger equations
Dynamical Systems
2017-11-08 v1
Abstract
The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schr\"odinger equation (DNLS) on finite one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of interactions going beyond the usual nearest-neighbour interaction. The problem of the existence of travelling wave solutions is converted into a fixed point problem for an operator on some appropriate function space which is solved by means of Schauder's Fixed Point Theorem.
Keywords
Cite
@article{arxiv.1707.08947,
title = {Periodic travelling wave solutions of discrete nonlinear Schr\"odinger equations},
author = {Dirk Hennig},
journal= {arXiv preprint arXiv:1707.08947},
year = {2017}
}