Similarity Analysis of Nonlinear Equations and Bases of Finite Wavelength Solitons
Abstract
We introduce a generalized similarity analysis which grants a qualitative description of the localised solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the solutions, and it is shown to be useful in analysing nonlinear structures like solitons, dublets, triplets, compact supported solitons and other patterns. We also introduce kinkantikink compact solutions for a nonlinearnonlinear dispersion equation, and we construct a basis of finite wavelength functions having selfsimilar properties.
 Publication:

International Journal of Modern Physics E
 Pub Date:
 2000
 DOI:
 10.1142/S0218301300000167
 arXiv:
 arXiv:mathph/0003030
 Bibcode:
 2000IJMPE...9..263L
 Keywords:

 Mathematical Physics;
 Mathematics  Dynamical Systems;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 18 pages Latex, 6 figures eps