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Compacton-like and kink-like waves for a higher-order wave equation of Korteweg-de Vries type. (English) Zbl 1134.35096

The authors deal with the generalized KdV equation considered by A. S. Fokas [On a class of physically important integrable equations, Physica D 87, 145–150 (1995)], written as
\[ v_{t} - \tfrac{3}{2} \beta \rho_{2} v_{xxt} + \beta (1 - \tfrac{3}{2} \rho_{2}) v_{xxx} + \alpha v v_{x} - \tfrac{1}{2} \alpha \beta \rho_{2} (v v_{xxx} + 2 v_{x} v_{xx}) = 0. \] Implicit compacton-like and kink-like solutions are obtained as travelling waves \(v = v(x - c t)\) passing through singular points. Results are tested by numerical integration.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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References:

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