Abstract: Solitons, kinks or breathers, are manifestations of weakly nonlinear excitations which, for instance, arise in weakly anharmonic mass-particle chains. In strongly anharmonic chains the tails of the emerging patterns decay at a super-exponential rate. In the continuum limit the tail zone shrinks into a singularity where the nonlinear dispersion due to discreteness degenerates and the resulting solitary waves become strictly compact. Hence their name: compactons. Unlike solitons, compactons may exist in any dimension. We shall show how multidimensional compactons emergence and interact. Some physical systems where such phenomena happen will be described. Notably, many of the compact patterns emerge in the continuum limit out of discrete dynamical systems. Such systems may be found in physics, biology or social sciences.

For a popular introduction see: What is a Compacton, Notices of the AMS, Vol. 52, #7, pp 738, 2005.

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