Compactons: Solitons with finite wavelength

Philip Rosenau*, James M. Hyman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg-de Vries-like equations wtih nonlinear dispersion: ut+(um)x+(un)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.

Original languageEnglish
Pages (from-to)564-567
Number of pages4
JournalPhysical Review Letters
Issue number5
StatePublished - 1993
Externally publishedYes


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