A KAM Theorem for Higher Dimensional Reversible Nonlinear Schrödinger Equations

Yingnan Sun; Zhaowei Lou; Jiansheng Geng

paper

A KAM Theorem for Higher Dimensional Reversible Nonlinear Schrödinger Equations

arXiv:1903.06862

Abstract

In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible (non-Hamiltonian) coupled nonlinear Schrödinger systems on $d -$ torus $T^{d}$ .

28 pages