Instability of Multi-Solitons for Derivative Nonlinear Schr{\"o}dinger Equations

Abstract

In [19] and [26], the authors proved the stability of multi-solitons for derivative nonlinear Schr{\"o}dinger equations. Roughly speaking, sum of finite stable solitons is stable. We predict that if there is one unstable solition then multi-soliton is unstable. This prediction is proved in [7] for classical nonlinear Schr{\"o}dinger equations. In this paper, we proved this prediction for derivative nonlinear Schr{\"o}dinger equations by using the method of C{\^o}te-Le Coz [7] with the help of Gauge transformation.