Center stable manifold for ground states of nonlinear Schrödinger equations with internal modes

2022/06/16 by Masaya Maeda, Maeda, Masaya, Yohei Yamazaki +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Laser-Matter Interactions and Applications #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2206.08156

openalex publication_date 2022/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of solutions of nonlinear Schrödinger equation near unstable ground states. The existence of the local center stable manifold around ground states and the asymptotic stability for the solutions on the manifold is proved. The novelty of our result is that we allow the existence of internal modes.

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