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A pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows. (English) Zbl 0953.65073
A pseudospectral approximation for general isotropic nonlinear wave equations is presented. A symmetric factorization of the linear part is followed by an exact integration in spectral space. The remaining nonlinear and forcing terms can be handled with any standard pseudospectral procedure. Solving the linear part exactly eliminates the stiffness of the original problem. The algorithm is tested on several problems of three-dimensional long surface waves: solitary wave propagation, interaction and diffraction.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
76M22 Spectral methods applied to problems in fluid mechanics
35L70 Second-order nonlinear hyperbolic equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25 Solitary waves for incompressible inviscid fluids
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