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

Екомасов, Е. Г.; Gumerov, A. M.; Kudryavtsev, R. V.

doi:10.1134/s0021364015120061

Cited by 14 publications

(13 citation statements)

References 9 publications

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“…As has been shown before, at the scattering of a DW by a defect a part of its energy is expended on the excitation of a nonlinear magnetization wave localized in the defect region, or a «magnetic breather» (if the DW leaves the defect) [21,33,34]. Moreover, the magnitude of this energy can vary depending on the initial velocity of the DW υ 0 .…”

Section: Dynamics Of Nonlinear Waves Localized In the Defect Regionmentioning

confidence: 91%

“…For instance, they often took into account the magnetic anisotropy modulation both for the case of point and extended defects [21,33]. It is shown that when a DW passes through a thin magnetic layer with a lower anisotropy value, high-amplitude localized nonlinear waves of magnetization can arise in it [19,33,34]. The amount of energy expended on the excitation of localized waves determine the effective damping of the moving DW and can vary depending on the DW initial velocity.…”

Section: Introductionmentioning

confidence: 99%

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Localized magnetic inhomogeneities generation on defects as a new channel of damping for a moving domain wall

Gumerov¹,

Екомасов²,

Kudryavtsev³

et al. 2018

LoM

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The paper presents theoretical studies on the domain wall energy losses that arise when it moves through the magnetic defect region. These losses are largely related to the generation of localized magnetization waves in the defect region. It is shown that the process of the domain wall energy scattering on the defect can be regarded as a new "channel of damping" for a domain wall. The study was carried out using numerical and analytical methods through the example of a three-layer model of the ferromagnetic structure, in which the intermediate layer differs in its physical parameters from the rest of the crystal. The intermediate layer (or magnetic defect) was simulated by a spatial modulation of the magnetic parameters. The modes of motion, in which "effective damping" is minimal, were calculated. The damping value depends on the excitation energy of the localized waves and is determined by the ratio of the defect properties and initial velocity of the domain wall motion. It is specifically shown that an increase in the domain wall energy loss is associated with the increase in the localized waves oscillations amplitude. In this case, the dependence of the localized waves oscillations amplitude on the domain wall initial velocity only has one maximum. It is at this point that the domain wall energy losses are maximal. They can be significantly reduced if the domain wall velocity is noticeably higher or lower than the maximum. This behavior was studied for both the point and extended defects.

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Section: Dynamics Of Nonlinear Waves Localized In the Defect Regionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Localized magnetic inhomogeneities generation on defects as a new channel of damping for a moving domain wall

Gumerov¹,

Екомасов²,

Kudryavtsev³

et al. 2018

LoM

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“…This equation was studied in [5,7] where the authors consider finite-dimensional reductions of it to understand the kink-like dynamics. As a first step, they consider solutions u of small amplitude of (3), which can be approximated by solutions of the linear partial differential equation (4) ∂ 2 t u − ∂ 2 x u + u = εδ(x)u, which has a family of wave solutions u im (x, t) given by (5) u im (x, t) = a(t)e −ε|x|/2 , where a(t) = a 0 cos(Ωt + θ 0 ), Ω = 1 − ε 2 /4 and im stands for impurity. The solution u im is not a traveling wave, but it is spatially localized at x = 0.…”

Section: Introductionmentioning

confidence: 99%

“…More details of this approach and its applications can be found in [5,7,16]. It is worth to mention that the finite dimensional reduction of PDE problems to ODE systems via an adequate ansatz and variational methods has been considered in an extensive range of works (see [4,6,8,9,10,24,25]). It remains as an open problem to prove that the solutions of the reduced system rigorously approximate the PDE solutions.…”

Section: Introductionmentioning

confidence: 99%

Critical velocity in kink-defect interaction models: Rigorous results

Gomide

Guàrdia

Seara

2020

Journal of Differential Equations

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In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More specifically, we prove that a heteroclinic orbit in the energy level 0 of a 2-dof Hamiltonian Hε is destroyed giving rise to heteroclinic connections between certain elements (at infinity) for exponentially small (in ε) energy levels. In this setting Melnikov theory does not apply because there are exponentially small phenomena.

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“…However, in the presence of perturbations, the structure of solitons can be changed and they can be more accurately described by deformable quasiparticles [5]. Soliton's internal degrees of freedom can be excited in this case and they can play a very important role in a number of physical processes [8][9][10][11][12]. Soliton internal modes can be responsible for the non-trivial effects of their interactions [13,14].…”

Section: Introductionmentioning

confidence: 99%