Traveling waves for nonlinear Schr\"odinger equations
Analysis of PDEs
2025-07-31 v2
Abstract
We look for traveling wave solutions to the nonlinear Schr\"odinger 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 the existence of its minimizers solving the nonlinear Schr\"odinger equation.
Cite
@article{arxiv.2406.03910,
title = {Traveling waves for nonlinear Schr\"odinger equations},
author = {Laura Baldelli and Bartosz Bieganowski and Jarosław Mederski},
journal= {arXiv preprint arXiv:2406.03910},
year = {2025}
}