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Approximations of solitary waves of the MRLW equation by B-spline finite elements. (English) Zbl 0893.35113

Summary: The modified regularized long wave equation is solved numerically by the \(B\)-spline finite element method. Three polynomial invariant conditions are reported. Solitary wave development, motion, and interaction are studied through computer simulation. Earlier estimates of the magnitude of the coefficient of inelasticity are confirmed. The development of a Maxwellian initial condition into solitary waves is shown to mimic that of the RLW equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76B25 Solitary waves for incompressible inviscid fluids
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs