2000/08/19 by A. Ludu, Ludu, A., R. F. O'Connell +3
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nuclear Theory (nucl-th) #Pattern Formation and Solitons (nlin.PS) #hep-th #math-ph #math.MP #nlin.PS #nlin.SI #nucl-th #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.nlin/0008026
27 pages TevTex, 7 figures .eps
arxiv created 2000/08/19 · arxiv updated 2009/11/30
We use a one-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. We also introduce kink-antikink compact solutions for the nonlinear-nonlinear dispersion K(2,2) equation, and we construct a basis of scaling functions similar with those used in the multiresolution analysis. These approaches are useful in describing nonlinear structures and patterns, as well as in the derivation of the time evolution of initial data for nonlinear equations with finite wavelength soliton solutions.