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Zbl 0952.35502
Rosenau, P.; Hyman, J.M.
Compactons: Solitons with finite wavelength. (English)
[J] Phys. Rev. Lett. 70, No.5, 564-567 (1993). ISSN 0031-9007; ISSN 1079-7114/e

Summary: To understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg-de Vries-like equations with nonlinear dispersion: $u_t+(u^m)_x+(u^n)_{xxx}=0,$ $m,n>1$. The solitary wave solutions of these equations have remarkable properties: They collide elastically, but unlike the Korteweg-de Vries $(m=2, n=1)$ solitons, they have compact support. When two ``compactons'' collide, the interaction site is marked by the birth of low-amplitude compacton-anticompacton pairs. These equations seem to have only a finite number of local conservation laws. Nevertheless, the behavior and the stability of these compactons is very similar to that observed in completely integrable systems.

MSC 2000:: *35Q51 Solitons
35Q53 KdV-like equations

Cited in: Zbl 1154.65365

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