High-speed Kinks in a generalized discrete φ4 model

Dmitriev, Sergey V. ; Khare, Avinash ; Kevrekidis, Panayotis G. ; Saxena, Avadh ; Hadžievski, Ljupco (2008) High-speed Kinks in a generalized discrete φ4 model Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 77 (5). 056603_1-056603_9. ISSN 1539-3755

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Official URL: http://pre.aps.org/abstract/PRE/v77/i5/e056603

Related URL: http://dx.doi.org/10.1103/PhysRevE.77.056603

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.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:83350
Deposited On:20 Feb 2012 06:35
Last Modified:19 May 2016 00:14

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