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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 -3 2βρ 2 v xxt +β(1-3 2ρ 2 )v xxx +αvv x -1 2αβρ 2 (vv xxx +2v x v xx )=0·

Implicit compacton-like and kink-like solutions are obtained as travelling waves v=v(x-ct) passing through singular points. Results are tested by numerical integration.

35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions
34C05Location of integral curves, singular points, limit cycles (ODE)