High-speed kinks in a generalized discrete $φ^4$ model

Details High-speed kinks in a generalized discrete $φ^4$ model High-speed kinks in a generalized discrete $φ^4$ model

2008-02-17

arxiv.org/abs/0802.2375v1

Phys.Rev.E77:056603,2008

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, 5 figures, submitted to a journal

Scientific paper

10.1103/PhysRevE.77.056603

We consider a generalized discrete $\phi^4$ 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.

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