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.
The equation has a travelling wave solution given by This has compact support in x, and so is a compacton.