Stability of multi-solitons for the derivative nonlinear Schrödinger equation

Stefan Le Coz (1) , Yifei Wu (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 TJU - Tianjin University

The nonlinear Schrödinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the energy space, under suitable assumptions on the speeds and frequencies of the composing solitons. The main ingredients of the proof are modulation theory, energy coercivity and monotonicity properties.

Mots clés: solitons; Derivative nonlinear Schrödinger equation; multi-solitons; stability

Domaines: Equations aux dérivées partielles [math.AP]

Stefan Le Coz, Yifei Wu. Stability of multi-solitons for the derivative nonlinear Schrödinger equation. International Mathematics Research Notices, 2018, 13, pp.4120-4170. ⟨hal-01366702⟩