2023/07/03 by Hiroyuki Hirayama, Masahiro Ikeda, Hirayama, Hiroyuki +1
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems
paper · doi:10.48550/arxiv.2307.00980
openalex publication_date 2023/07/03 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28
We consider the Cauchy problem of the system of nonlinear Schrödinger 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 1-dimension.