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arXiv · 1407.0910

Quasi-periodic Solutions of a Derivative Nonlinear Schrödinger Equation

Jie Liu
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Abstract

This paper is concerned with a one dimensional (1D) derivative nonlinear Schrödinger equation with periodic boundary conditions \begin{equation*} \mi u_t+u_{xx}+\mi |u|^2u_x=0, \ \ x\in \mathbb{T}:=\mathbb{R}/2π\mathbb{Z}. \end{equation*} We 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.

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Jie Liu. 2014-07-03. Quasi-periodic Solutions of a Derivative Nonlinear Schrödinger Equation. https://doi.org/10.1080/00036811.2015.1032942

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