Compactons: Solitons with finite wavelength
- 1 February 1993
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 70 (5), 564-567
- https://doi.org/10.1103/physrevlett.70.564
Abstract
The understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg–de Vries–like equations wtih nonlinear dispersion: +( +( =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.
Keywords
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