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Solitary waves of the regularised long-wave equation. (English) Zbl 0717.65072

Authors’ summary: A finite element solution of the regularized long wave equation, based on Galerkin’s method using cubic splines as element shape functions, is set up. A linear stability analysis shows the scheme to be unconditionally stable. Test problems, including the migration and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evolution of a Maxwellian initial pulse is then studied.
Reviewer: W.Ames

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35L70 Second-order nonlinear hyperbolic equations

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References:

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