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A numerical study of \(K(3,2)\) equation. (English) Zbl 0988.65078

The paper deals with finite difference and finite element methods for numerical solution of the \(K(3,2)\) equation \(u_t+(u^3)_x+(u^2)_{xxx}=0\). The attention is paid to solitary wave solutions with compact support (compactons). The authors develop two numerical schemes and analyze their accuracy and stability. Numerical examples are presented.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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References:

[1] Abramowitz M., Handbook of Mathematical Functions (1970)
[2] Bullough R.K., Solitons (1980)
[3] Ismail, M.S. and Taha, T. A numerical study of Korteweg-de Vries like equations. Proceedings of the 15th Imacs World Congress on Scientific Computation Modelling and Applied Mathematics.
[4] DOI: 10.1016/S0378-4754(98)00132-3 · Zbl 0932.65096 · doi:10.1016/S0378-4754(98)00132-3
[5] DOI: 10.1080/00207160008804933 · Zbl 0955.65065 · doi:10.1080/00207160008804933
[6] Remoissenet M., Wave called solitons, concepts and experiments (1996) · Zbl 0922.35147
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