Variational problems for the system of nonlinear Schr\"odinger equations with derivative nonlinearities
Analysis of PDEs
2023-07-06 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
We consider the Cauchy problem of the system of nonlinear Schr\"odinger equations with derivative nonlinearlity. This system was introduced by Colin-Colin (2004) as a model of laser-plasma interactions. We study existence of ground state solutions and the global well-posedness of this system by using the variational methods. We also consider the stability of traveling waves for this system. These problems are proposed by Colin-Colin as the open problems. We give a subset of the ground-states set which satisfies the condition of stability. In particular, we prove the stability of the set of traveling waves with small speed for -dimension.
Cite
@article{arxiv.2307.00980,
title = {Variational problems for the system of nonlinear Schr\"odinger equations with derivative nonlinearities},
author = {Hiroyuki Hirayama and Masahiro Ikeda},
journal= {arXiv preprint arXiv:2307.00980},
year = {2023}
}
Comments
Introduction is modified and references are updated