On the Travelling Waves for the Generalized Nonlinear Schrödinger Equation

Abstract EN

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.