Existence and construction of compacton solutions

In this work we show the existence of compacton structures created from genuinely nonlinear dispersive equations. We show that the compactons, the compactly supported solitary waves free of exponential wings that vanish outside a finite core, are formally constructed from the focusing branches of these equations. We further show that the defocusing branches of these models generate solitary patterns solutions with infinite slopes or cusps. (C) 2003 Elsevier Ltd. All rights reserved.