TY - JOUR
T1 - Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
JF - Nonlinearity
Y1 - 2012
A1 - Massimiliano Berti
A1 - Philippe Bolle
AB - We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd.
VL - 25
N1 - cited By (since 1996)3
ER -