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 mn > 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.

Example

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The equation

 

has a travelling wave solution given by

 

This has compact support in x, and so is a compacton.

See also

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References

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  • 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, 70 (5), American Physical Society: 564–567, Bibcode:1993PhRvL..70..564R, doi:10.1103/PhysRevLett.70.564, PMID 10054146
  • Comte, Jean-Christophe (2002), "Exact discrete breather compactons in nonlinear Klein-Gordon lattices", Physical Review E, 65 (6), American Physical Society: 067601, Bibcode:2002PhRvE..65f7601C, doi:10.1103/PhysRevE.65.067601, PMID 12188877