Homoclinic standing waves in focusing DNLS equations
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.
Received: February 2010; Revised: July 2011; Published: August 2011.
2011 Impact Factor.913