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Álvarez, J.; Durán, A.

A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models. (English) Zbl 1209.65098

J. Comput. Appl. Math. 235, No. 7, 1790-1797 (2011).
Summary: A numerical method for simulating periodic travelling-wave solutions of some nonlinear dispersive wave equations is proposed. The construction of the scheme is based on an efficient computation of the elements that characterize these solutions: the initial profile and the velocity of the wave.

Cited in 3 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
76B25 Solitary waves for incompressible inviscid fluids

Keywords:

periodic travelling waves; Petviashvili’s method; conserved quantities; conservative methods; projection methods; numerical examples; Fourier pseudospectral method; Korteweg-de Vries equation; nonlinear dispersive wave equations
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References:

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