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Journal of Applied Mathematics
Volume 2017, Article ID 3694103, 5 pages
Research Article

Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations

Erich-Steinfurth-Str. 10/11, 16227 Eberswalde, Germany

Correspondence should be addressed to Dirk Hennig; ed.nilreb-uh.kisyhp@dginneh

Received 29 August 2017; Revised 24 October 2017; Accepted 7 November 2017; Published 26 November 2017

Academic Editor: Erik Van Vleck

Copyright © 2017 Dirk Hennig. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.