On the construction of almost periodic solutions for the derivative nonlinear Schrödinger equation

Abstract

In this paper, we consider a derivative nonlinear Schrödinger equation $$\mathrm{i}{\partial }_{t}u+{\partial }_{xx}u-V\ast u+\mathrm{i}|u{|}^2{\partial }_{x}u=0$$ on the torus $\mathbb{T}$, depending on some potential $V$. We prove that for `almost all' potentials $V$, this equation admits an almost-periodic solution.