Periodic and quasi-periodic solutions of a derivative nonlinear Schrödinger equation

Abstract

This paper is concerned with a one dimensional (1D) derivative nonlinear Schrödinger equation with periodic boundary conditionsWe show that above equation admits a family of real analytic quasi-periodic solutions with two Diophantine frequencies. The proof is based on a partial Birkhoff normal form and KAM method.

Invariant tori of a nonlinear Schrödinger equation with quasi-periodically unbounded perturbations

“…Later Liu [25] considered Chen-Liu-Lee equation, another class of derivative nonlinear Schrödinger equation, iu t + u xx + i|u| 2 u x = 0 under periodic boundary conditions. Using the same method in [14], they obtain the real analytic quasi-periodic solutions with only two Diophantine frequencies and the real analytic periodic solutions.…”