Non-linearity and self-similarity: Patterns and clusters
We introduce a qualitative similarity analysis, which yields relations between the geometry and kinematics of traveling localized solutions, associated to certain non-linear equations. This method predicts the existence of solitons, compactons, dublets, triplets, as well as other non-linear patterns. A finit supported wavelet-like frame is constructed in terms of compacton kink-antikink (KAK) solutions. © 2001 IMACS. Published by Elsevier Science. All rights reserved.