Fourier-Galerkin method for 2D solitons of Boussinesq equation

Authors:
M. A. Christou;C. I. Christov
Affiliations:
Department of Mathematics, University of Cyprus, Cyprus;Department of Mathematics, University of Louisiana at Lafayette, LA, USA
Venue:
Mathematics and Computers in Simulation
Year:
2007

Citing 6
Cited 3

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A fourier-series method for solving soliton problems

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The orthogonal rational functions of Higgins and Christov and algebraically mapped Chebyshev polynomials

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Fourier-Galerkin method for interacting localized waves

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Interacting localized waves for the regularized long wave equation via a Galerkin spectral method

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On the numerical simulation of unsteady solutions for the 2D Boussinesq paradigm equation

NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions

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Original article: Numerical implementation of the asymptotic boundary conditions for steadily propagating 2D solitons of Boussinesq type equations

Mathematics and Computers in Simulation

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Abstract

We develop a Fourier-Galerkin spectral technique for computing the stationary solutions of 2D generalized wave equations. To this end a special complete orthonormal system of functions in L^2(-~,~) is used for which product formula is available. The exponential rate of convergence is shown. As a featuring example we consider the Proper Boussinesq Equation (PBE) in 2D and obtain the shapes of the stationary propagating localized waves. The technique is thoroughly validated and compared to other numerical results when possible.