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| Starting from the nonlinear 3d gravity water wave problem of finite depth (without surface tension), we consider two small amplitude-modulated plane wave solutions of the linearized problem with different phase in the asymptotic regime where the smallness parameter and the scaling coefficient of macroscopic time and space are the same. In order to observe the macroscopic interaction of two arbitrary carrier waves we derive the corresponding system of modulation equations up to second order in the scaling coefficient and discuss its justification. |
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