# American Institute of Mathematical Sciences

June  2012, 32(6): 2101-2123. doi: 10.3934/dcds.2012.32.2101

## Quasi-periodic solutions for derivative nonlinear Schrödinger equation

 1 School of Science, Shanghai Second Polytechnic University, Shanghai 201209, China 2 School of Mathematical Sciences, Fudan University, Shanghai 200433

Received  February 2011 Revised  June 2011 Published  February 2012

In this paper, we discuss the existence of time quasi-periodic solutions for the derivative nonlinear Schrödinger equation $$\label{1.1}\mathbf{i} u_t+u_{xx}+\mathbf{i} f(x,u,\bar{u})u_x+g(x,u,\bar{u})=0$$ subject to Dirichlet boundary conditions. Using an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field and Birkhoff normal form, we will prove that there exist a Cantorian branch of KAM tori and thus many time quasi-periodic solutions for the above equation.
Citation: Meina Gao, Jianjun Liu. Quasi-periodic solutions for derivative nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2012, 32 (6) : 2101-2123. doi: 10.3934/dcds.2012.32.2101
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