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Center for Nonlinear Studies |
We present a systematic study of the scattering properties of a kink-antikink pair for five different disctetizations of the phi4 model in terms of amount of radiation and collisions. I will first talk about different nonlinearities and different types of excitations in soliton-bearing nonlinear equations. The continuum phi4 model is one of the prototypical and the simplest model in field theory and phase transitions. A discrete analog of this model can be created in several different ways depending on the desired properties, e.g. absence of a discreteness (i.e. Peierls-Nabarro) barrier to kink motion, existence of exact solutions, etc. We have systematically comapared the properties of fundamental solutions of five different discretizations including the nature of kink type solitary waves, the role of kink internal modes and the spectral properties of the linearization around such waves. We studied these features as a function of lattice spacing, initial kink velocity and distance as one deviates from the continuumm limit and observed/analyzed many interesting nonlinear phenomena.