Homoclinic standing waves in focusing DNLS equations

Pages: 737 - 752, Volume 31, Issue 3, November 2011

doi:10.3934/dcds.2011.31.737       Abstract        References        Full Text (5208.8K)       Related Articles

Michael Herrmann - Universität des Saarlandes, FR Mathematik, Postfach 15 11 50, D-66041 Saarbrücken, Germany (email)

Abstract: We study focusing discrete nonlinear Schrödinger equations and present a novel variational existence proof for homoclinic standing waves (bright solitons). Our approach relies on the constrained maximization of an energy functional and provides the existence of two one-parameter families of waves with unimodal and even profile function for a wide class of nonlinearities. Finally, we illustrate our results by numerical simulations.

Keywords:  Discrete nonlinear Schrödinger equation (DNLS), nonlinear lattice waves, homoclinic standing waves, solitary waves, bright solitons, breathers.
Mathematics Subject Classification:  Primary: 37K60, 47J30; Secondary: 78A40.

Received: February 2010;      Revised: July 2011;      Published: August 2011.

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