Asymptotic stability of solitary waves for the 1D cubic-quintic Schrödinger equation with no internal mode

Abstract

For the Schrödinger equation with a cubic-quintic, focusing-defocusing nonlinearity in one space dimension, we prove the asymptotic stability of solitary waves for a large range of admissible frequencies. For this model, the linearized problem around the solitary waves does not have internal mode nor resonance.

References in corpus (3)

• Orbital stability vs. scattering in the cubic-quintic Schrodinger equation
• Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary Waves
• Long-time dynamics of small solutions to 1$d$ cubic nonlinear Schrödinger equations with a trapping potential

Cited by in corpus (1)

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