Travelling waves of forced discrete nonlinearSchrödinger equations

Michal Fečkan; Vassilis M. Rothos

doi:10.3934/dcdss.2011.4.1129

Article Contents

2011, Volume 4, Issue 5: 1129-1145. Doi: 10.3934/dcdss.2011.4.1129

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Travelling waves of forced discrete nonlinear Schrödinger equations

Michal Fečkan^1, and
Vassilis M. Rothos^2,

1.
Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava
2.
School of Mathematics, Physics and Computational Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124

Received: August 31, 2009

Revised: December 31, 2009

Published: September 2011

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Abstract

We address the existence and bifurcation of periodic travelling wave solutions in forced spatially discrete nonlinear Schrödinger equations with local interactions. We consider polynomial type and bounded nonlinearities. The mathematical methods are based in using Palais-Smale conditions and variational methods. Some generalizations are also discussed.

Keywords:

Mathematics Subject Classification: Primary: 34K14, 37K60; Secondary: 37L60.

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