arXiv subjects

Petr A. Blinov

Publications and source records attributed to Petr A. Blinov.

6 recordsLinked to original sources

arXiv2025

Long-range interaction of kinks in higher-order polynomial models

We obtain asymptotic estimates of the interaction forces between kink and antikink in a family of field-theoretic models with two vacua in (1+1)-dimensional space-time. In our study we consider a new class of soliton solutions previously found in our paper [Chaos, Solitons and Fractals 165 (2022) 112805]. We focus on the case of kinks having one exponential and one power-law asymptotics. We show that if the kink and antikink are faced each other with long-range tails, the force of attraction between them at large separations demonstrates a power-law decay with the distance. We also performed numerical simulations to measure the interaction force and obtained good agreement between the experimental values and theoretical estimates.

hep-th↗

arXiv2022

Kinks in higher-order polynomial models

We consider a family of field-theoretic models with a real scalar field in (1+1)-dimensional space-time. The field dynamics in each model is determined by a polynomial potential with two degenerate minima. We obtain exact general formulas for kink solutions with power-law asymptotic behavior. We also write out formulas for the asymptotics of all found kinks. In addition, we analyze some other properties of the obtained kinks: stability potentials, zero modes, positions of the centers of mass.

hep-th↗

arXiv2022

Deformations of Kink Tails

We study the asymptotic properties of kinks in connection with the deformation procedure. We show that, upon deformation of the field-theoretic model, the asymptotics of kinks can change or remain unchanged, depending on the properties of the deforming function. The cases of both explicit and implicit kinks are considered. In addition, we show that the the deformation procedure can be applied to the important case of implicit kinks. We also prove that for any kink with a power-law tail, the stability potential decreases as the inverse square of the coordinate. The physical consequences of the deformation are discussed: the change of the kink mass, as well as the asymptotic behavior of the kink-antikink force.

hep-th↗

arXiv2020

From thin to thick domain walls: An example of the $φ^8$ model

We demonstrate that for some certain values of parameters of the $(1+1)$-dimensional $φ^8$ model, the kink solutions can be found from polynomial equations. For some selected values of the parameters we give the explicit formulas for the kinks in all topological sectors of the model. Based on the obtained algebraic equations, we show that in a special limiting case, kinks with power-law asymptotics arise in the model, describing, in particular, thick domain walls. Objects of this kind could be of interest for modern cosmology.

hep-th↗

arXiv2020

Domain wall thickness and deformations of the field model

We consider the change in the asymptotic behavior of solutions of the type of flat domain walls (i.e., kink solutions) in field-theoretic models with a real scalar field. We show that when the model is deformed by a bounded deforming function, the exponential asymptotics of the corresponding kink solutions remain exponential, while the power-law ones remain power-law. However, the parameters of these asymptotics, which are related to the wall thickness, can change.

hep-th↗

arXiv2020

Explicit kinks in higher-order field theories

We study an example of higher-order field-theoretic model with an eighth-degree polynomial potential -- the $φ^8$ model. We show that for some certain ratios of constants of the potential, the problem of finding kink-type solutions in $(1+1)$-dimensional space-time reduces to solving algebraic equations. For two different ratios of the constants, which determine positions of the vacua, we obtained explicit formulas for kinks in all topological sectors. The properties of the obtained kinks are also studied -- their masses are calculated, and the excitation spectra which could be responsible for the appearance of resonance phenomena in kink-antikink scattering are found.

hep-th↗