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

Abstract

For the Schrödinger 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 Schrödinger 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.

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References in corpus (5)

• Quadratic Klein-Gordon equations with a potential in one dimension
• Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities
• Long-time dynamics of small solutions to 1$d$ cubic nonlinear Schrödinger equations with a trapping potential
• Asymptotic Stability of Solitary Waves for One Dimensional Nonlinear Schrödinger Equations
• Asymptotic stability of the fourth order ${\varphi }^4$ kink for general perturbations in the energy space

Cited by in corpus (1)

• Collision of two solitons for $1d$ Nonlinear Schrodinger Equation with the same mass