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Zbl 1052.35511
Rosenau, Philip
On nonanalytic solitary waves formed by a nonlinear dispersion.
(English)
[J] Phys. Lett., A 230, No. 5-6, 305-318 (1997). ISSN 0375-9601

Summary: We study the prototypical, genuinely nonlinear, $K(m,n)$ equation, $u_t\pm a(u^m)_x+(u^n)_{xxx}=0$, $a=\text{const}$, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein $m=n+2$ is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the $K(m,n)$ can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For $n<0$ the enhanced dispersion at the tail may generate algebraically decaying patterns.
MSC 2000:
*35Q51 Solitons

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