A KAM result on compact Lie groups

TL;DR

This paper discusses recent advances in finding quasi-periodic solutions for Hamiltonian PDEs on compact manifolds, with specific stability results for nonlinear Schrödinger equations on SU(2) and SO(3).

Contribution

It provides new existence results for quasi-periodic solutions and establishes linear stability for certain nonlinear Schrödinger equations on specific compact Lie groups.

Findings

Existence of quasi-periodic solutions for Hamiltonian PDEs on compact manifolds.

Linear stability of nonlinear Schrödinger equations on SU(2) and SO(3).

Abstract

We describe some recent results on existence of quasi-periodic solutions of Hamiltonian PDEs on compact manifolds. We prove a linear stability result for the non-linear Schr\"odinger equation in the case of $SU(2)$ and $SO(3)$.