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.

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Cited by in corpus (1)

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