Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations. (26th November 2017)

• Record Type: Journal Article
• Authors: Hennig, Dirk
• Other Names: Van Vleck Erik Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2017(2017)
• Publication Date: 2017-11-26
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2017/3694103
• Languages: English
• ISSNs: 1110-757X

Abstract

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.