The effect of dissipation on solutions of the generalized Korteweg-de Vries equation

DOI10.1016/0377-0427(96)00021-0zbMath0869.65059OpenAlexW2110243019MaRDI QIDQ2564253

Ohannes A. Karakashian, William R. McKinney, Jerry L. Bona, Vassilios A. Dougalis

Publication date: 1 September 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(96)00021-0

zbMATH Keywords

finite element methodnonlinear wavesnumerical experimentsRunge-Kutta methodsemidiscretizationKorteweg-de Vries equationblow upsingularity formation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves, On the stability of solitary-wave solutions of model equations for long waves, Numerical study of the generalized Korteweg-de Vries equations with oscillating nonlinearities and boundary conditions, Sound–ultrasound interaction in bubbly fluids: Theory and possible applications, Computations of blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation, Damping to prevent the blow-up of the Korteweg-de Vries equation, Asymptotic decomposition of nonlinear, dispersive wave equations with dissipation, Nonlinear boundary control of the unforced generalized Korteweg-de Vries-Burgers equation, Zero-Dissipation Limit for Nonlinear Waves, A qualitative study and numerical simulations for a time-delayed dispersive equation, Simulation of blow-up solutions to the generalized KdV equations by moving collocation methods, Stabilization of the Korteweg-de Vries-Burgers equation with non-periodic boundary feedbacks

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