Fourier-Galerkin method for 2D solitons of Boussinesq equation

DOI10.1016/j.matcom.2006.10.002zbMath1107.65343OpenAlexW2052252058MaRDI QIDQ871063

Christo I. Christov, Marios A. Christou

Publication date: 15 March 2007

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2006.10.002

zbMATH Keywords

convergencenumerical resultsBoussinesq equationsolitonswave equationsstationary solutionsGalerkin spectral method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Soliton equations (35Q51)

Related Items (11)

Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions ⋮ Waves in microstructured solids and the Boussinesq paradigm ⋮ Perturbation solution for the 2D Boussinesq equation ⋮ Invariant preserving schemes for double dispersion equations ⋮ Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions ⋮ Numerical implementation of the asymptotic boundary conditions for steadily propagating 2D solitons of Boussinesq type equations ⋮ On the pseudolocalized solutions in multi-dimension of Boussinesq equation ⋮ Time-dependent solution for natural convection in a porous enclosure using the Darcy-Lapwood-Brinkman model ⋮ On the Numerical Simulation of Unsteady Solutions for the 2D Boussinesq Paradigm Equation ⋮ Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms ⋮ Unnamed Item

Cites Work

• Fourier-Galerkin method for localized solutions of the sixth-order generalized Boussinesq equation
• Asymptotic coefficients of Hermite function series
• Spectral methods using rational basis functions on an infinite interval
• Interacting localized waves for the regularized long wave equation via a Galerkin spectral method
• The orthogonal rational functions of Higgins and Christov and algebraically mapped Chebyshev polynomials
• A Fourier-Series Method for Solving Soliton Problems
• A Complete Orthonormal System of Functions in $L^2 ( - \infty ,\infty )$ Space
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