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

Yvan Martel

Vol. 3 (2022), No. 4, 839–867
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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Keywords
solitary wave, stability, asymptotic stability, Schrödinger equation
Mathematical Subject Classification
Primary: 35B40, 35Q51, 35Q55, 37K40
Milestones
Received: 4 October 2021
Accepted: 25 May 2022
Published: 21 February 2023
Authors
Yvan Martel
Centre de Mathématiques Laurent Schwartz
Ecole polytechnique
Institut Polytechnique de Paris
Palaiseau
France