Electron. J. Differential Equations, Vol. 2022 (2022), No. 69, pp. 1-25.

A KAM theorem for higher dimensional reversible nonlinear Schrodinger equations

Zhaowei Lou, Yingnan Sun

Abstract:
In this article we prove an abstract Kolmogorov-Arnold-Moser (KAM) theorem for infinite dimensional reversible systems. Using this theorem, we obtain the existence of quasi-periodic solutions for a class of reversible (non-Hamiltonian) coupled nonlinear Schrodinger systems on a d-torus.

Submitted May 2, 2022. Published October 10, 2022.
Math Subject Classifications: 37K55, 35B15.
Key Words: KAM theorem; reversible vector field; quasi-periodic solution; nonlinear Schrodinger equation.
DOI: https://doi.org/10.58997/ejde.2022.69

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Zhaowei Lou
School of Mathematics
Nanjing University of Aeronautics and Astronautics
Nanjing 211106, China
email: zwlou@nuaa.edu.cn
Yingnan Sun
School of Mathematics
Nanjing University of Aeronautics and Astronautics
Nanjing 211106, China
email: sunyingnan@nuaa.edu.cn

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