A KAM result on compact Lie groups

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 Schrödinger equation in the case of $SU(2)$ and $SO(3)$.

20 pages, 1 figure

References in corpus (5)

• Quasi-periodic solutions for fully nonlinear forced reversible Schroedinger equations
• Sobolev quasi periodic solutions of multidimensional wave equations with a multiplicative potential
• An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifold
• Quasi-Töplitz functions in KAM theorem
• The energy graph of the non linear Schrödinger equation

Cited by in corpus (4)

• On time dependent Schr{ö}dinger equations: global well-posedness and growth of Sobolev norms
• Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential
• Quasi-periodic solutions for the forced Kirchhoff equation on ${\mathbb{T}}^d$
• Long time stability of small finite gap solutions of the cubic Nonlinear Schrödinger equation on ${\mathbb{T}}^2$