Generation and excitation of a magnetic soliton in a three-layer ferromagnet using dc magnetic fields and weak ac fields in the presence of dissipation in the system have been considered. An analysis of the solutions to the equation of motion in an ac field shows the possibility of increasing the magnetic-soliton amplitude with time under certain conditions. The resonance effect is also affected by the geometric parameters of the thin layer: the translational mode of soliton oscillations is excited at a large layer width.

The generation and excitation of a magnetic soliton in a three-layer ferromagnet by constant magnetic fields and fields of variable frequency and small amplitude in the presence of dissipation in the system are considered. The analysis of the solutions of the equation of motion in an alternating field shows the possibility of increasing the amplitude of the magnetic soliton over time under certain conditions. The resonant effect is also affected by the geometric parameters of the thin layer: at a large layer width, the translational mode of the soliton oscillations is also excited.

The generation and autoresonant excitation of a magnetic breather in a three-layer ferromagnet by fields of variable frequency and small amplitude in the presence of dissipation in the system is considered. The ferromagnetic structure consists of two wide identical layers separated by a thin layer with modified values of the magnetic anisotropy parameter. The anisotropy parameters are considered functions of the coordinate directed perpendicular to the layer interface. In the one-dimensional case, the function of the anisotropy parameter is modeled in the form of a rectangle. The external magnetic field is variable in time with a small amplitude and frequency, which is a linear function of time. The obtained equation of motion for magnetization in the form of a sine-Gordon equation was solved numerically using an explicit integration scheme. The distribution of magnetization at the initial time was set in the form of a Bloch domain boundary, located far from a thin layer. At certain values of the parameters of a thin layer, when a domain wall passes at a constant speed through it, a magnetic inhomogeneity is formed in the form of a magnetic breather. In the absence of an external field, the breather amplitude decays with time. An analysis of the solutions of the equation of motion in an alternating field shows the possibility, under certain conditions, of increasing with time the amplitude of the magnetic breather. For each case of magnetic anisotropy parameter values, there is a threshold value of the magnetic field amplitude leading to resonance. The resonance effect is also affected by the geometric parameters of a thin layer: with a decrease in the width of the layer, the amplitude of the breather increases more slowly in time. With a large layer width, the translational mode of breather oscillations is also excited.

Abstract Based on the experience of developing hard-to-recover oil reserves in fields, a new technology has been proposed that allows increasing the productivity of producing horizontal wells by creating HFF cross cracks and minimizing the risks of auto-HFF cracks fracturing from injection wells.

Summary The paper presents the results of: 1) various technologies testing for the development of low-permeability reservoirs using horizontal wells with multi-stage hydraulic fracturing of formation (HW with MHFF); 2) the increase of the repeated fracturing operations efficiency in vertical wells by taking into account geomechanical effects. The marker and geophysical methods for determining the flow profile of the HW with MHFF are compared with the calculations results of the hydrodynamic model. The results were applied to determine the optimal types of well completion, planned to further improvement of approaches to the development of low-permeability oil deposits. Also the technological capabilities of the flow profile research methods of and the directions of their further development were determined.

We study properties of the localized solutions to the sine‐Gordon equation excited on the attractive impurity by a moving kink. The cases of one‐dimensional and two‐dimensional spatially extended impurities are considered. For the case of one‐dimensional impurity the possibility of excitation of the first even and odd high‐amplitude impurity modes by the moving kink is demonstrated. By linearizing the sine‐Gordon equation the dispersion relations for the small‐amplitude localized impurity modes were obtained. The numerically obtained dispersion relations in the case of low oscillation amplitudes are in a good agreement with the results of analytical calculations. For the case of two‐dimensional impurity we show the possibility of excitation of the nonlinear high‐amplitude waves of new type called here a breathing pulson and a breathing 2D soliton. We suggest analytical expressions to model these nonlinear excitations. The breathing pulson and breathing 2D soliton are long‐lived and can be of both symmetric and asymmetric type depending on the impurity type. The range of the impurity parameters where the breathing pulson and breathing 2D soliton can be excited was determined. The dependencies of the oscillation frequency and the amplitude of the excited impurity modes on the impurity parameters are reported. Copyright © 2016 John Wiley & Sons, Ltd.

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.

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.

Исследована динамика солитонов уравнения синус-Гордона при наличии внешней силы, затухания и пространственной модуляции периодического потенциала. С помощью численных методов показана возможность генерации локализованных нелинейных волн солитонного и бризерного типа. Изучена их эволюция и найдены зависимости амплитуды и частоты колебаний от параметров системы. Библ. 50. Фиг. 7.

The one-dimensional nonlinear dynamics of a domain wall under the effect of an external dc magnetic field in three-layer ferromagnets with different values of the parameters of magnetic anisotropy and exchange in the layers has been studied theoretically. Equations of motion for the coordinate of the center of a domain wall and for the velocity of its motion after passage from one layer into another has been found using perturbation-theory methods. It is shown that, in the case of small defects, the analytical results agree well with the numerical results. The minimum velocity required for a domain wall to pass from one layer into another has been found numerically as a function of the parameters of the material.

Experimental and theoretical investigations of solitary domain wall dynamics in an yttrium orthoferrite plate under the action of a pulse magnetic field were carried out. The investigations are performed under conditions in which the change in the gradient magnetic field is comparable to the magnitude of the pulse magnetic field shifting the domain walls when the latter are displaced from their equilibrium position.

Теоретически изучена одномерная нелинейная динамика доменной границы под действием внешнего постоянного магнитного поля в трехслойном ферромагнетике с разными значениями параметров магнитной анизотропии и обмена в слоях. С помощью методов теории возмущений найдены уравнения движения для координаты центра доменной границы и скорости ее движения после перехода из одного слоя в другой. Показано, что для случая малых дефектов аналитические результаты хорошо согласуются с численными. Найдены численные зависимости минимальной скорости, необходимой доменной границе для перехода из одного слоя в другой, от параметров материала.

We study properties of the localized solitons to the sine-Gordon equation excited on the attractive impurity by a moving kink. The cases of one- and two-dimensional spatially extended impurities are considered. For the case of one-dimensional impurity the possibility of excitation of the first even and odd high-amplitude impurity modes by the moving kink is demonstrated. For the case of two-dimensional impurity we show the possibility of excitation of the nonlinear high-amplitude waves of new type called here breathing pulson and breathing 2D soliton. We suggest different analytical expressions to model these nonlinear excitations. The dependencies of the oscillation frequency and the amplitude of the excited impurity modes on the impurity parameters are reported.

In the article the dynamics of a passage of a kink through a point defect is investigatedanalytically and numerically. The dependence of the minimum velocity necessary for going through the inhomogeneous region has been obtained from the parameters of the system. The translational and pulsation modes of the kink are calculated. The origin and evolution of the nonlinear wave of the weakly damped breather appearing after the passage of a kink through a point defect are investigated. There are compared the known analytical and numerical results.

Theoretically investigated the origin and evolution of the three types of dynamic magnetic inhomogeneities (a breather, breather transforming into a soliton, and a soliton), appearing in a flat layer of the parameters of magnetic anisotropy and exchange interaction, different from the parameters in the main area of the infinite in a ferromagnetic after the passage of the 180-degree domain wall. Found the values of parameters, which determine the possibility of the existence of each of the magnetic inhomogeneities. For the magnetic inhomogeneities of the types damped quiescent breather and soliton obtained dependence of the amplitude and frequency of oscillations of the parameters of the defect.

We investigate analytically and numerically the structure and properties of localized two- and three-kink solutions of the sine-Gordon equation, which are excited in the region of the attracting impurity. We have considered cases of single and double spatially extended impurity.