Traveling waves for nonlinear Schrödinger equations
Abstract
We look for traveling wave solutions to the nonlinear Schrödinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a Sobolev-type inequality involving the momentum and we show the existence of its minimizers solving the nonlinear Schrödinger equation.
Fields of Study & Subjects
Nonlinear Photonic Systems
Advanced Mathematical Physics Problems
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4781–4797
- Publication date
- 13 May 2026
- Language
- EN