On the travelling waves for the generalized nonlinear schrodinger equation

Abstract

This paper is devoted to the analysis of the travelling waves for a class of generalized nonlinear Schrodinger 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.