High-speed kinks in a generalized discrete phi(4) model

SV Dmitriev
A Khare
PG Kevrekidis, University of Massachusetts - Amherst
A Saxena
L Hadzievski

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This is the prepublished version harvested from ArXiv. The published version is located at http://pre.aps.org/abstract/PRE/v77/i5/e056603

Abstract

We consider a generalized discrete ϕ4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity. The constructed exact moving solutions are dependent on the specific value of the propagation velocity. We demonstrate that in this class of models, given a specific velocity, the problem of finding the exact moving solution is integrable. Namely, this problem originally expressed as a three-point map can be reduced to a two-point map, from which the exact moving solutions can be derived iteratively. It was also found that these high-speed kinks can be stable and robust against perturbations introduced in the initial conditions.