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Nonlinear refraction-diffraction of waves in shallow water. (English) Zbl 0593.76028

Summary: The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K-P equation [B. B. Kadomtsev and V. I. Petviashvili, Dokl. Akad. Nauk SSSR 192, 753-756 (1970; Zbl 0217.250)] to include varying depth in two dimensions. Comparisons are made between present numerical results, experimental data and previous numerical calculations.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q99 Partial differential equations of mathematical physics and other areas of application
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0217.250
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References:

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