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arXiv · 1707.08947

Periodic travelling wave solutions of discrete nonlinear Schr\"odinger equations

Dirk Hennig
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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.

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Dirk Hennig. 2017-07-27. Periodic travelling wave solutions of discrete nonlinear Schr\"odinger equations. https://arxiv.org/abs/1707.08947

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