In the theory of integrable systems, a compacton (introduced in ) 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.

Example

The equation

has a travelling wave solution given by

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

See also

• Peakon

• Vector soliton

References