Traveling waves for nonlinear Schr\"odinger equations
Laura Baldelli, Bartosz Bieganowski, Jaros{\l}aw Mederski
TL;DR
This paper investigates the existence of traveling wave solutions to the nonlinear Schrödinger equation with subsonic speeds across various physical models, using a novel Sobolev-type inequality approach.
Contribution
It introduces a new Sobolev-type inequality involving momentum and proves the existence of minimizers that solve the nonlinear Schrödinger equation.
Findings
Existence of traveling wave solutions for subsonic speeds.
Development of a Sobolev-type inequality involving momentum.
Identification of minimizers solving the nonlinear Schrödinger equation.
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.
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Taxonomy
TopicsNonlinear Photonic Systems · Advanced Mathematical Physics Problems · Quantum Mechanics and Non-Hermitian Physics