Abstract



Solitons kinks and the like are manifestation of weakly nonlinear
excitations in action. On the other hand strongly nonlinear phenomena
(say, vibration of a genuinely anharmonic lattice) exhibit a completly
different solitary  patterns, which as a rule are nonanalytic. The 
compacton, a soliton, or a breather, with a compact support, is a 
typical example of such phenomenon wherein the nonlinear dispersion 
degenerates at the edge of the pulse and confines the pulse to a 
finite domain. Some of these compactons travel and collide elastically. 
Other compact structures have a fixed support (equalibria or breathers). 
Certain compacton-supporting cases can be related to the conventional 
concept of integrabilty, but most of these phenomena are represent 
completly novel structures. A typical novel structure is that of a compact 
breather generated by an anharmonic lattice embedded in a specific
site potential.