A Fourier-Series Method for Solving Soliton Problems

DOI10.1137/0911037zbMath0707.65090OpenAlexW2029433548MaRDI QIDQ3489402

K. L. Bekyarov, Christo I. Christov

Publication date: 1990

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0911037

zbMATH Keywords

convergencesolitonsKuramoto-Sivashinsky equationKorteweg-de Vries equationspectral methodFourier-Galerkin methodorthonormal system of functionsFourier-series methodBrent 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) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Applications to the sciences (65Z05)

Related Items (11)

A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation ⋮ Kawahara solitons in Boussinesq equations using a robust Christov-Galerkin spectral method ⋮ A Hermite spectral method for the computation of homoclinic orbits and associated functionals ⋮ The orthogonal rational functions of Higgins and Christov and algebraically mapped Chebyshev polynomials ⋮ Fourier-Galerkin method for 2D solitons of Boussinesq equation ⋮ Fourier-Galerkin numerical technique for solitary waves of fifth order Korteweg-de Vries equation ⋮ 2D solitons in Boussinesq equation with dissipation ⋮ Interacting localized waves for the regularized long wave equation via a Galerkin spectral method ⋮ Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics ⋮ Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms ⋮ The eigenvalues of Hermite and rational spectral differentiation matrices

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