An abstract infinite dimensional KAM theorem with application to nonlinear higher dimensional Schrodinger equation systems

2017/01/20 by Shidi Zhou, Zhou, Shidi
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Photonic Systems #Numerical methods for differential equations #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1701.05727

openalex publication_date 2017/01/20 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28

Abstract

In this paper we consider nonlinear Schrodinger systems with periodic boundary condition in high dimension. We establish an abstract infinite dimensional KAM theorem and apply it to the nonlinear Schrodinger equation systems with real Fourier Multiplier. By establishing a block-diagonal normal form, We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.

Citations

• Newton's method and periodic solutions of nonlinear wave equations

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