Construction of multi-solitons and multi kink-solitons of derivative nonlinear Schr{\"o}dinger equations

TL;DR

This paper constructs multi-soliton and multi kink-soliton solutions for derivative nonlinear Schrödinger equations, demonstrating their existence and asymptotic behavior using fixed point methods and Strichartz estimates.

Contribution

It introduces a novel approach to prove the existence of multi-solitons and multi kink-solitons for derivative nonlinear Schrödinger equations.

Findings

Existence of multi-soliton solutions established.

Existence of multi kink-soliton solutions demonstrated.

Solutions behave as sums of solitons at large times.

Abstract

We look for solutions to derivative nonlinear Schrodinger equations built upon solitons. We prove the existence of multi-solitons 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 sum of solitons i.e multi kink-solitons. Our proofs proceed by fixed point arguments around the desired profile, using Strichartz estimates.