On a generalized derivative nonlinear Schrödinger equation

Abstract

We consider a generalized derivative nonlinear Schr\''odinger equation. We prove existence of wave operator under an explicit smallness of the given asymptotic states. Our method bases on studying the associated system used in \cite{Tinpaper4}. Moreover, we show that if the initial data is small enough in $H^2(\mathbb{R})$ then the associated solution scatters up to a Gauge transformation.