A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham's equation family

DOI10.1016/S0021-9991(03)00203-1zbMath1027.65136OpenAlexW2090386765MaRDI QIDQ1401136

John P. Boyd

Publication date: 17 August 2003

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-9991(03)00203-1

zbMATH Keywords

cnoidal wavesWhitham equationpseudospectral algorithmCorner wavestravelling waves with corners

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

IDSOLVER: a general purpose solver for \(n\)th-order integro-differential equations, The Legendre-Burgers equation: when artificial dissipation fails, A numerical study of the Whitham equation as a model for steady surface water waves, Near-corner waves of the Camassa-Holm equation, Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation, Explicit solutions of the reduced Ostrovsky equation, The cnoidal wave/corner wave/breaking wave scenario: a one-sided infinite-dimension bifurca\-tion, Fourier pseudospectral method with Kepler mapping for travelling waves with discontinuous slope: application to corner waves of the Ostrovsky-Hunter equation and equatorial Kelvin waves in the four-mode approximation, Kelvin waves in the nonlinear shallow water equations on the sphere: nonlinear travelling waves and the corner wave bifurcation, Fourier pseudospectral method with Kepler mapping for travelling waves with discontinuous slope: Application to corner waves of the Ostrovsky-Hunter equation and equatorial Kelvin waves in the four-mode approximation, Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations

Uses Software

• Differentiation Matrix Suite

Cites Work

• Solitons from sine waves: Analytical and numerical methods for non- integrable solitary and cnoidal waves
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• Resonant Triads Involving a Nondispersive Wave
• A note on the breaking of waves
• Variational methods and applications to water waves
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions
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