Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations

The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schrödinger equation (DNLS) on 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 prob...

Full description

Saved in:
Bibliographic Details
Main Author: Dirk Hennig
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2017/3694103
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850234561684832256
author Dirk Hennig
author_facet Dirk Hennig
author_sort Dirk Hennig
collection DOAJ
description The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schrödinger equation (DNLS) on 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.
format Article
id doaj-art-1673ff65f4c84818a5d000054dc56c92
institution OA Journals
issn 1110-757X
1687-0042
language English
publishDate 2017-01-01
publisher Wiley
record_format Article
series Journal of Applied Mathematics
spelling doaj-art-1673ff65f4c84818a5d000054dc56c922025-08-20T02:02:37ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/36941033694103Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger EquationsDirk Hennig0Institut für Physik, Humboldt Universität zu Berlin, Erich-Steinfurth-Str. 10/11, 16227 Eberswalde, GermanyThe existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schrödinger equation (DNLS) on 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.http://dx.doi.org/10.1155/2017/3694103
spellingShingle Dirk Hennig
Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
Journal of Applied Mathematics
title Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
title_full Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
title_fullStr Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
title_full_unstemmed Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
title_short Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
title_sort periodic travelling wave solutions of discrete nonlinear schrodinger equations
url http://dx.doi.org/10.1155/2017/3694103
work_keys_str_mv AT dirkhennig periodictravellingwavesolutionsofdiscretenonlinearschrodingerequations