A KAM Theorem for Higher Dimensional Reversible Nonlinear Schr\"{o}dinger Equations

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 Schr\"{o}dinger systems on $d-$torus $\mathbb{T}^d$.