@article {2011,
title = {Nonlinear wave and Schr{\"o}dinger equations on compact Lie groups and homogeneous spaces},
journal = {Duke Mathematical Journal},
volume = {159},
year = {2011},
month = {2011},
chapter = {479},
abstract = {We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr{\textasciidieresis}odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.},
issn = {0012-7094},
doi = {10.1215/00127094-1433403},
author = {Massimiliano Berti and Michela Procesi}
}