01296nas a2200145   4500008004100000022001300041245010400054210006900158300001400227490000700241520073600248100002400984700002001008856012201028       2012                        eng d  a0951771500aSobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential0 aSobolev quasiperiodic solutions of multidimensional wave equatio  a2579-26130 v253 aWe 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.1 aBerti, Massimiliano1 aBolle, Philippe  uhttps://www.math.sissa.it/publication/sobolev-quasi-periodic-solutions-multidimensional-wave-equations-multiplicative