A. M. Gumerov

Structure and properties of four-kink multisolitons of the sine-Gordon equation

The dynamics of nonlinear waves of the sine-Gordon equation with a spatially modulated periodic potential are studied using analytical and numerical methods. The structure and properties of four-kink multisolitons excited on two identical attracting impurities are determined. For small-amplitude oscillations, an analytical spectrum of the oscillations is obtained, which is in qualitatively agreement with the numerical results.

Transformation of SineGordon Solitons in Models with Variable Coefficients and Damping

The dynamics of sine-Gordon solitons in the presence of an external force, damping, and a spatially modulated periodic potential is studied. Numerical methods are used to show the possibility of generating localized nonlinear waves of the soliton and breather types. Their evolution is investigated, and the dependences of the amplitude and the oscillation frequency on the parameters of the system are found.

Simulation of the Nonlinear Dynamics of Magnetic Inhomogeneities in Real Magnets

The dynamics of domain walls (DW) in an infinite ferromagnet containing a flat layer with parameters of magnetic anisotropy and exchange interaction differing from the bulk values was investigated. The dependences of the minimum velocity of DW transmission through the defect region and the translational and pulsation modes of DW fluctuations on the parameters describing the inhomogeneity of magnetic anisotropy and exchange interaction were found.

Resonant Dynamics of the Domain Walls in Multilayer Ferromagnetic Structure

The domain walls dynamics and generation and evolution of magnetic inhomogeneities of soliton type, emerging in a thin flat layer with the parameters of the magnetic anisotropy, which are different from other two thick layers of the five-layer ferromagnetic structure, were investigated.

Resonance dynamics of kinks in the sine-Gordon model with impurity, external force and damping

We study the resonance dynamics of the sine-Gordon equation kinks with a point impurity. We consider the possibility of localized nonlinear waves generation on the impurities. By using analytical and numerical methods we show that the damping and external force counteract the development of kink resonant reflection from the attracting impurity. However, the underlying causea resonant energy exchange between solitonsstill occurs.

On the possibility of the observation of the resonance interaction between kinks of the sine-Gordon equation and localized waves in real physical systems

The resonance dynamics of kinks of the sine-Gordon equation in a system with a single point impurity with allowance for the generation of localized waves in the presence of an external force and dissipation has been studied. Equations of motion for the coordinate of the kink center and the amplitude of the impurity mode have been found. The analysis of solutions of these equations and results of the numerical simulation of the modified sine-Gordon equation have showed that damping and the external force act against the appearance of the resonance reflection of the kink from the attractive impurity. However, the resonance energy exchange between solitons causing it still takes place.

Numerical simulation of the generation of multisoliton type magnetic inhomogeneities in ferromagnets with inhomogeneous parameters

The generation and evolution of multisoliton type magnetic inhomogeneities, which appear in two flat layers with the magnetic anisotropy that are different from those in three thick layers after pinning a 180° domain wall, have been investigated theoretically. The structure of the multisoliton type magnetic inhomogeneities have been constructed for the revealed magnetic inhomogeneities, and the ranges of the parameters determining the possibility of their existence have been found.