Special Session 113: New Achievements in Nonlinear PDEs and Applications

Travelling waves for nonlinear Schrodinger equations
Bartosz Bieganowski
University of Warsaw
Poland
Co-Author(s):    Laura Baldelli, Jaroslaw Mederski
Abstract:
We look for travelling wave solutions to the nonlinear Schrodinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a variant of Sobolev type inequality involving the momentum and we show existence of its minimizers solving the nonlinear Schrodinger equation.