TY  - JOUR
AU  - Dmitriev, Sergey V.
AU  - Khare, Avinash
AU  - Kevrekidis, Panayotis G.
AU  - Saxena, Avadh
AU  - Hadžievski, Ljupčo
PY  - 2008
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3466
AB  - 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.
T2  - Physical Review E
T1  - High-speed kinks in a generalized discrete phi(4) model
VL  - 77
IS  - 5
DO  - 10.1103/PhysRevE.77.056603
ER  - 

@article{
author = "Dmitriev, Sergey V. and Khare, Avinash and Kevrekidis, Panayotis G. and Saxena, Avadh and Hadžievski, Ljupčo",
year = "2008",
abstract = "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.",
journal = "Physical Review E",
title = "High-speed kinks in a generalized discrete phi(4) model",
volume = "77",
number = "5",
doi = "10.1103/PhysRevE.77.056603"
}

Dmitriev, S. V., Khare, A., Kevrekidis, P. G., Saxena, A.,& Hadžievski, L.. (2008). High-speed kinks in a generalized discrete phi(4) model. in Physical Review E, 77(5).
https://doi.org/10.1103/PhysRevE.77.056603

Dmitriev SV, Khare A, Kevrekidis PG, Saxena A, Hadžievski L. High-speed kinks in a generalized discrete phi(4) model. in Physical Review E. 2008;77(5).
doi:10.1103/PhysRevE.77.056603 .

Dmitriev, Sergey V., Khare, Avinash, Kevrekidis, Panayotis G., Saxena, Avadh, Hadžievski, Ljupčo, "High-speed kinks in a generalized discrete phi(4) model" in Physical Review E, 77, no. 5 (2008),
https://doi.org/10.1103/PhysRevE.77.056603 . .