Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation

• 成果类型: Article
• 署名作者: Martel, Yvan
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01270-4
• 发表日期: 2024
• 页码: 1253-1328
• 关键词: nonlinear schrodinger-equations; ground-states; solitons; SCATTERING; DYNAMICS; instability; Operators

摘要

For the Schr & ouml;dinger equation with a cubic-quintic, focusing-focusing nonlinearity in one space dimension, this article proves the local asymptotic completeness of the family of small standing solitary waves under even perturbations in the energy space. For this model, perturbative of the integrable cubic Schr & ouml;dinger equation for small solutions, the linearized equation around a small solitary wave has an internal mode, whose contribution to the dynamics is handled by the Fermi golden rule.