Error analysis of a spectral projection of the Benjamin-Ono equation

DOI10.1007/s10543-005-2636-xzbMath1075.76048OpenAlexW2071017305MaRDI QIDQ2568623

Henrik Kalisch

Publication date: 18 October 2005

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-005-2636-x

zbMATH Keywords

solitary wavescollocation approximationFourier-Galerkin semi-discretizations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Spectral methods applied to problems in fluid mechanics (76M22) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (12)

Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions ⋮ Derivation and comparison of model equations for interfacial capillary-gravity waves in deep water ⋮ Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity ⋮ On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation ⋮ Numerical bifurcation for the capillary Whitham equation ⋮ A two-grid spectral method to study of dynamics of dense discrete systems governed by Rosenau-Burgers' equation ⋮ On uniqueness results for solutions of the Benjamin equation ⋮ The regularized Benjamin-Ono and BBM equations: well-posedness and nonlinear stability ⋮ Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. II: Dynamics ⋮ Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I: Approximations ⋮ ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED ⋮ Well-posedness and ill-posedness results for the regularized Benjamin-Ono equation in weighted Sobolev spaces

Cites Work

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• Error analysis for spectral approximation of the Korteweg-de Vries equation
• Stability of the Fourier Method
• Spectral and Pseudo Spectral Methods for Advection Equations
• Spectral Methods for a Nonlinear Initial Value Problem Involving Pseudo Differential Operators
• Internal waves of permanent form in fluids of great depth
• Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

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