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Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations

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  • Dirk Hennig

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.

Suggested Citation

  • Dirk Hennig, 2017. "Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-5, November.
    • Handle: RePEc:hin:jnljam:3694103
    DOI: 10.1155/2017/3694103
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