In the theory of integrable systems, a compacton, introduced in (Philip Rosenau & James M. Hyman 1993), is a soliton with compact support.
An example of an equation with compacton solutions is the generalization
of the Korteweg–de Vries equation (KdV equation) with m, n > 1. The case with m = n is the Rosenau–Hyman equation as used in their 1993 study; the case m = 2, n = 1 is essentially the KdV equation.
has a travelling wave solution given by
This has compact support in x, so is a compacton.
- Rosenau, Philip (2005), "What is a compacton?" (PDF), Notices of the American Mathematical Society: 738–739
- Rosenau, Philip; Hyman, James M. (1993), "Compactons: Solitons with finite wavelength", Physical Review Letters, American Physical Society, 70 (5): 564–567, Bibcode:1993PhRvL..70..564R, doi:10.1103/PhysRevLett.70.564, PMID 10054146