Abstract and Applied Analysis
Volume 2011 (2011), Article ID 181369, 12 pages
Research Article

On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation

Department of Mathematics, Faculty of Arts and Sciences, Doğuş University, 34722 Istanbul, Turkey

Received 25 February 2011; Accepted 5 May 2011

Academic Editor: Ondřej Došlý

Copyright © 2011 Mahir Hasanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is devoted to the analysis of the travelling waves for a class of generalized nonlinear Schrödinger equations in a cylindric domain. Searching for travelling waves reduces the problem to the multiparameter eigenvalue problems for a class of perturbed p-Laplacians. We study dispersion relations between the eigenparameters, quantitative analysis of eigenfunctions and discuss some variational principles for eigenvalues of perturbed p-Laplacians. In this paper we analyze the Dirichlet, Neumann, No-flux, Robin and Steklov boundary value problems. Particularly, a “duality principle” between the Robin and the Steklov problems is presented.