Construction of the multi-soliton trains, multi kink-soliton trains of the derivative nonlinear Schr\"odinger equations by the fixed point method

Phan van Tin (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We look for solutions to derivative nonlinear Schrodinger equations built upon ¨ solitons. We prove the existence of multi-soliton trains i.e. solutions behaving at large time as the sum of finite solitons. We also show that one can attach a kink at the begin of the train i.e multi kink-soliton trains. Our proofs proceed by fixed point arguments around the desired profile, using Strichartz estimates.

Domaines: Equations aux dérivées partielles [math.AP]

Phan van Tin. Construction of the multi-soliton trains, multi kink-soliton trains of the derivative nonlinear Schr\"odinger equations by the fixed point method. 2021. ⟨hal-03126096v2⟩