Dynamics of magnetic kinks in exchange-coupled ferromagnetic layers

Шамсутдинов, М. А.; Habibullin, I. T.; Kharisov, A. T.; Tankeyev, A. P.

doi:10.1134/s0031918x09100020

Cited by 4 publications

(4 citation statements)

References 15 publications

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“…To obtain the lattice equation for ω j n , it is necessary to get rid of the variable u j n by means of the relations ( 7) and (9).…”

Section: Local Conservation Laws and Miura-type Transformationsmentioning

confidence: 99%

“…More precisely, the sequence of Laplace invariants satisfies some integrable differential-difference equations of the form (1), related by a point transformation to Equation (L7) from the list below. Such lattices can find application in studying the nonlinear dynamics of localized magnetic inhomogeneities in such magnetically ordered substances as ferromagnets, antiferromagnets with weak ferromagnetism, and magnetoelastic and magnetoelectric interactions [9,10]. Equations of the type under consideration have potential applications in the problem of describing dislocations in media with a microstructure, as well as in the nonlinear theory of elastic and nonelastic deformations accompanied with the deep reconstruction of an initially ideal lattice: the switching of interatomic bonds, the changing of the class of symmetry, the formation of new phases, singular defects and heterogeneities, and the fragmentation of the lattice (see, for instance, [11,12]).…”

Section: Introductionmentioning

confidence: 99%

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Miura-Type Transformations for Integrable Lattices in 3D

2023

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This article studies a class of integrable semi-discrete equations with one continuous and two discrete independent variables. At present, in the literature there are nine integrable equations of the form un+1,xj=f(un,xj,unj+1,unj,un+1j,un+1j−1) up to point transformations. An efficient method based on some relation that generalizes the notion of the local conservation law is proposed for searching for Miura-type transformations relating to semi-discrete equations in 3D. The efficiency of the method is illustrated with the equations from the list. For one of the equations, which is little studied, the continuum limit is calculated. For this equation, the problem of finite-field reductions in the form of Darboux integrable systems of equations of a hyperbolic type is discussed. For reductions of small orders, N=1 and N=2, complete sets of characteristic integrals are presented. Note that the existence of characteristic integrals makes it possible to construct particular solutions to the original lattice. For the case N=1, an explicit solution was found in this paper. A new semi-discrete equation is found that lies beyond the considered class. For this equation, the Lax pair is presented.

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“…To obtain the lattice equation for ω j n , it is necessary to get rid of the variable u j n by means of the relations ( 7) and (9).…”

Section: Local Conservation Laws and Miura-type Transformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Miura-Type Transformations for Integrable Lattices in 3D

2023

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“…Soliton solutions of nonlinear differential equations attract increased attention of researchers because of an increasing use in physical applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. For example, solitons of the sine-Gordon equation(the SGE) are frequently used.…”

Section: Introductionmentioning

confidence: 99%

Excitation of Large-Amplitude Localized Nonlinear Waves by the Interaction of Kinks of the Sine-Gordon Equation with Attracting Impurity

Gumerov¹,

Екомасов²,

Kudryavtsev³

et al. 2019

Nelin. Dinam.

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The generation and evolution of localized waves on an impurity in the scattering of a kink of the sine-Gordon 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

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“…More precisely, the sequence of Laplace invariants satisfies some integrable differential-difference equation of the form (1.1), related by a point transformation to equation 7) from the list below. Such chains can find application in studying the nonlinear dynamics of localized magnetic inhomogeneities in such magnetically ordered substances as ferromagnets, antiferromagnets with weak ferromagnetism, magnetoelastic and magnetoelectric interactions [10], [11]. Equations of the type under consideration have potential applications in the problem of describing dislocations in media with a microstructure, as well as in the nonlinear theory of elastic and nonelastic deformations accompanied with deep reconstruction of an initially ideal lattice: switching of interatomic bonds, changing of the class of symmetry, formation of new phases, singular defects and heterogeneities, fragmentation of the lattice (see, for instance, [12], [13]).…”

Section: Introductionmentioning

confidence: 99%