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Fourier–Galerkin method for 2D solitons of Boussinesq equation

Author

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  • Christou, M.A.
  • Christov, C.I.

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 L2(−∞,∞) 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.

Suggested Citation

  • Christou, M.A. & Christov, C.I., 2007. "Fourier–Galerkin method for 2D solitons of Boussinesq equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 82-92.
    • Handle: RePEc:eee:matcom:v:74:y:2007:i:2:p:82-92
    DOI: 10.1016/j.matcom.2006.10.002
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    Cited by:

    1. Christov, Christo I., 2012. "Numerical implementation of the asymptotic boundary conditions for steadily propagating 2D solitons of Boussinesq type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1079-1092.
    2. Amin, Fahs & Zakeri, Ali & Wanko, Adrien, 2021. "Time-dependent solution for natural convection in a porous enclosure using the Darcy–Lapwood–Brinkman model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 39-65.

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