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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.


The equation

has a travelling wave solution given by

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

See also[edit]