 1220 Massimiliano Berti, Philippe Bolle
 Sobolev quasi periodic solutions of multidimensional
wave equations with a multiplicative potential
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Feb 11, 12

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Abstract. We prove the existence of quasiperiodic solutions for wave equations with a multiplicative
potential on T^d, d \ge 1, and finitely differentiable nonlinearities, quasiperiodically 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 NashMoser 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 nonresonance conditions than in [11]
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