Similarity analysis of nonlinear equations and bases of finite wavelength solitons

We introduce a generalized similarity analysis which grants a qualitative d escription of the localised solutions of any nonlinear differential equatio n. This procedure provides relations between amplitude, width, and velocity of the solutions, and it is shown to be useful in analysing nonlinear stru ctures like solitons, dublets, triplets, compact supported solitons and oth er patterns. We also introduce kink-antikink compact solutions for a nonlin ear-nonlinear dispersion equation, and we construct a basis of finite wavel ength functions having self-similar properties.