Article ID Journal Published Year Pages File Type
4609429 Journal of Differential Equations 2016 29 Pages PDF
Abstract

We consider the capillary-gravity water wave problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly amplitude-modulated plane wave solutions of the linearized problem in the absence of quadratic and cubic resonances. We justify the derived system of macroscopic equations in the case of gravity waves using the stability of the finite depth water wave problem on the time scale O(1/ϵ)O(1/ϵ).

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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