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2017 Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
Dirk Hennig
J. Appl. Math. 2017: 1-5 (2017). DOI: 10.1155/2017/3694103

Abstract

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.

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Dirk Hennig. "Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations." J. Appl. Math. 2017 1 - 5, 2017. https://doi.org/10.1155/2017/3694103

Information

Received: 29 August 2017; Revised: 24 October 2017; Accepted: 7 November 2017; Published: 2017
First available in Project Euclid: 14 December 2017

zbMATH: 07037474
MathSciNet: MR3740174
Digital Object Identifier: 10.1155/2017/3694103

Rights: Copyright © 2017 Hindawi

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