Evgenii Ekomasov
450076, Ufa, Zaki Validi Street, 32
Bashkir State University, theoretical physics department
Publications:
Fakhretdinov M. I., Samsonov K. Y., Dmitriev S. V., Ekomasov E. G.
Attractive Impurity as a Generator of Wobbling Kinks and Breathers in the $\varphi^4$ Model
2024, Vol. 20, no. 1, pp. 1526
Abstract
The $\varphi^4$ theory is widely used in many areas of physics, from cosmology and elementary particle physics to biophysics and condensed matter theory. However, in the $\varphi^4$ model, there are no spatially localized solutions in the form of breathers. Topological defects, or kinks, in this theory describe stable, solitary wave excitations. In practice, these excitations, as they propagate, necessarily interact with impurities or imperfections in the onsite potential. In this work, with the help of numerical calculations using the method of lines, the interaction of the kink in the $\varphi^4$ model with extended impurities is considered. The case of an attractive rectangular impurity is analyzed. It is found that after the kinkimpurity interaction, an internal mode with frequency $\sqrt{\frac32}$ is excited on the kink and it becomes a wobbling kink. It is shown that with the help of kinkimpurity interaction, an extended rectangular attracting impurity, as well as a point impurity, can be used as a generator for excitation of longlived highamplitude localized breather waves. The structure of the excited wobbling breather (or wobbler), which consists of a compact core and an extended tail, is described. It is shown that the wobbler tail has the form of a spatially unbounded quasisinusoidal function with a classical frequency $\sqrt{2}$. To determine the lifetime of the wobbler, the dependence of the amplitude of the impurity mode on time is found. For the case of small impurities, it turned out that it practically does not change for a long time. For the case of large impurities, the wobbler amplitude begins to noticeably decrease with time. The frequency of wobbler oscillations does not depend on the initial velocity of the kink. The dependence of the impurity mode oscillation amplitude on the initial kink velocity has minima and maxima. By changing the impurity parameters, one can also control the dynamic parameters of the wobbler. A linear approximation is considered that allows an analytical solution of the problem for localized breather waves, and the limits of its applicability for this model are found.

Fakhretdinov M. I., Samsonov K. Y., Dmitriev S. V., Ekomasov E. G.
Kink Dynamics in the $\varphi^4$ Model with Extended Impurity
2023, Vol. 19, no. 3, pp. 303320
Abstract
The $\varphi^4$ theory is widely used in many areas of physics, from cosmology and elementary
particle physics to biophysics and condensed matter theory. Topological defects, or kinks, in
this theory describe stable, solitary wave excitations. In practice, these excitations, as they
propagate, necessarily interact with impurities or imperfections in the onsite potential. In this
work, we focus on the effect of the length and strength of a rectangular impurity on the kink
dynamics. It is found that the interaction of a kink with an extended impurity is qualitatively
similar to the interaction with a wellstudied point impurity described by the delta function,
but significant quantitative differences are observed. The interaction of kinks with an extended
impurity described by a rectangular function is studied numerically. All possible scenarios of
kink dynamics are determined and described, taking into account resonance effects. The inelastic
interaction of the kink with the repulsive impurity arises only at high initial kink velocities. The
dependencies of the critical and resonant velocities of the kink on the impurity parameters are
found. It is shown that the critical velocity of the repulsive impurity passage is proportional to
the square root of the barrier area, as in the case of the sineGordon equation with an impurity.
It is shown that the resonant interaction in the $\varphi^4$ model with an attracting extended impurity,
as well as for the case of a point impurity, in contrast to the case of the sineGordon equation, is
due to the fact that the kink interacts not only with the impurity mode, but also with the kink’s
internal mode. It is found that the dependence of the kink final velocity on the initial one has
a large number of resonant windows.

Ekomasov E. G., Nazarov V. N., Samsonov K. Y.
Changing the Dynamic Parameters of Localized Breather and Soliton Waves in the SineGordon Model with Extended Impurity, External Force, and Decay in the Autoresonance Mode
2022, Vol. 18, no. 2, pp. 217229
Abstract
Possibility of changing the dynamic parameters of localized breather and soliton waves for
the sineGordon equation in the model with extended impurity, variable external force and dissipation
was investigated using the autoresonance method. The model of ferromagnetic structure
consisting of two wide identical layers separated by a thin layer with modified values of magnetic
anisotropy parameter was taken as a basis. Frequency of external field is a linear function of time.
The sineGordon equation (SGE) was solved numerically using the finite differences method with
explicit scheme of integration. For certain values of the extended impurity parameters a magnetic
inhomogeneity in the form of magnetic breather is formed when domain wall passes through it
with constant velocity. The numerical simulation showed that using special variable force and
small amplitude it is possible to resonantly increase the amplitude of breather. For each case
of the impurity parameters values, there is a threshold value of the magnetic field amplitude
leading to resonance. Geometric parameters of thin layer also have influence on the resonance
effect — for decreasing layer width the breather amplitude grows more slowly. For large layer
width the translation mode of breather oscillations is also excited. For certain parameters of
extended impurity, a soliton can form. For a special type of variable field with frequency linearly
dependent on time, soliton is switched to antisoliton and vice versa.

Gumerov A. M., Ekomasov E. G., Kudryavtsev R. V., Fakhretdinov M. I.
Excitation of LargeAmplitude Localized Nonlinear Waves by the Interaction of Kinks of the SineGordon Equation with Attracting Impurity
2019, Vol. 15, no. 1, pp. 2134
Abstract
The generation and evolution of localized waves on an impurity in the scattering of a kink of the sineGordon equation are studied. It is shown that the problem can be considered as excitation of oscillations of a harmonic oscillator by a short external impulse. The external impulse is modeled by the scattering of a kink on an impurity. The influence of the modes of motion of a kink on the excitation energy of localized waves is numerically and analytically studied. The method of collective coordinate for the analytical study is used. The value of this energy is determined by the ratio of the impurity parameters and the initial kink velocity. It is shown that the dependence of the energy (and amplitude) of the generated localized waves on the initial kink velocity has only one maximum. This behavior is observed for the cases of point and extended impurities. Analytical expression for the amplitude of the localized wave in the case of point impurity is obtained. This allows controlling the excitation energy of localized
waves using the initial kink velocity and impurity parameters. The study of the evolution of localized impurities under the action of an external force and damping has shown a good agreement with the nondissipative case. It is shown that small values of the external force have no significant effect on the oscillations of localized waves. An analytical expression for the logarithmic decrement of damping is obtained. This study may help to control the parameters of the excited waves in real physical systems.

Fakhretdinov M. I., Zakirianov F. K., Ekomasov E. G.
Discrete breathers and multibreathers in the PeyrardBishop DNA model
2015, Vol. 11, No. 1, pp. 7787
Abstract
Discrete breathers and multibreathers are investigated within the Peyrard–Bishop model. Region of existence of discrete breathers and multibreathers is defined. One, two and three site discrete breathers solutions are obtained. Their properties and stability are investigated.
