Standing waves on infinite depth

Abstract

The two-dimensional standing wave problem, for an infinitely deep layer, is considered, based on the formulation of the problem as a second order non local PDE. Despite the presence of infinitely many resonances in the linearized problem, we use the Nash–Moser implicit function theorem to prove the existence of standing waves corresponding to values of the amplitude ε having 0 as a Lebesgue point. To cite this article: G. Iooss et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).