Multimodal Standing Gravity Waves: a Completely Resonant System

Abstract : The standing gravity wave problem on an infinitely deep fluid layer is considered under the form of a nonlinear non local scalar PDE of second order as in [6]. Nonreso-nance at quadratic order of the infinite dimensional bifurcation equation, allows to give the explicit form of the quadratic change of variables able to suppress quadratic terms in the nonlinear equation. We state precisely the equivalence between formulations in showing that the above unbounded change of variable is invertible. The infinite set of solutions which can be expanded in powers of amplitude ε is then given up to order ε 2 .
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Gérard Iooss, Pavel Plotnikov. Multimodal Standing Gravity Waves: a Completely Resonant System. Journal of Mathematical Fluid Mechanics, Springer Verlag, 2005, 7 (S), pp.17. 〈10.1007/s00021-004-0128-4〉. 〈hal-01265187〉

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