Dynamics of solitons in a domain wall in a ferromagnet

Zvezdin, A. K.; Popkov, A. F.; Chetkin, M. V.

doi:10.1070/pu1992v035n12abeh002284

Cited by 26 publications

(42 citation statements)

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“…are the respective dimensionless parameters of diffraction, self-interaction, and loss, in which The nonlinear coefficient, , for an exchange-free nonlinear Schrodinger envelope equation can be determined using expansion in series by small amplitudes of the nonlinear dispersion equation [12] or by means of bilinear relationships analogical to the energy conservation law [13]. Estimates show that for antennae into those that pertain to "effective straight line antennae".…”

Section: Arc Antenna Creation Of Linear and Nonlinear Structures Withmentioning

confidence: 99%

Excitation of vortices using linear and nonlinear magnetostatic waves

et al. 2005

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It is shown that stationary vortex structures can be excited in a ferrite film. This is the first proposal for creating vortex structures in the important cm and mm wavelength ranges. It is shown that both linear and nonlinear structures can be excited using a three-beam interaction created with circular antennae. These give rise to a special phase distribution created by linear and nonlinear mixing. An interesting set of three clockwise rotating vortices joined by one counter-rotating one presents itself in the linear regime: a scenario that is only qualitatively changed by the onset of nonlinearity. It is pointed out that control of the vortex structure, through parametric coupling, based upon a microwave resonator, is possible and that there are many interesting possibilities for applications. …………………………………………………………………………………… PACS number(s) : 41.20Jb, 42.25Bs, 78.20.Bh

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Section: Arc Antenna Creation Of Linear and Nonlinear Structures Withmentioning

confidence: 99%

Excitation of vortices using linear and nonlinear magnetostatic waves

et al. 2005

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“…[16,17,18] it was shown that, in the case of single-component magnon wave function, the evolution of the envelope is described by the nonlinear Schrödinger equation. In a similar way, for two components Ψ ± one arrives at a system of phenomenological equations of the GPE/CGL type, which include the above-mentioned source terms, written below as −f δ(z) to allow analytical treatment of the problem (numerical results will be reported below for a realistic broad shape of the source).…”

Section: The Modelmentioning

confidence: 99%

“…It should be emphasized that only condensed magnons, with the above-mentioned values of the frequency and wavenumbers, (ω 0 , ±k 0 ), contribute to this magnetization, whereas all other magnons merely decrease the absolute value of the static magnetization. Following the envelope (slowly-varying-amplitude) approximation, widely adopted for the analysis of nonlinear spin waves in ferromagnetic films [16,17,18], as well for the description of nonlinear waves in many other settings, we introduce the order parameter (the full wave function of magnons)…”

Section: The Modelmentioning

confidence: 99%

Ginzburg-Landau model of Bose-Einstein condensation of magnons

et al. 2010

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We introduce a system of phenomenological equations for Bose-Einstein condensates of magnons in the one-dimensional setting. The nonlinearly coupled equations, written for amplitudes of the right-and left-traveling waves, combine basic features of the Gross-Pitaevskii and complex Ginzburg-Landau models. They include localized source terms, to represent the microwave magnon-pumping field. With the source represented by the δ-functions, we find analytical solutions for symmetric localized states of the magnon condensates. We also predict the existence of asymmetric states with unequal amplitudes of the two components. Numerical simulations demonstrate that all analytically found solutions are stable. With the δ-function terms replaced by broader sources, the simulations reveal a transition from the single-peak stationary symmetric states to multi-peak ones, generated by the modulational instability of extended nonlinear-wave patterns. In the simulations, symmetric initial conditions always converge to symmetric stationary patterns. On the other hand, asymmetric inputs may generate nonstationary asymmetric localized solutions, in the form of traveling or standing waves. Comparison with experimental results demonstrates that the phenomenological equations provide for a reasonably good model for the description of the spatiotemporal dynamics of magnon condensates.

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“…The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice. DOI: 10.1103/PhysRevLett.118.044103 The nonlinear Schrödinger equation (NLSE) [5], and Bose-Einstein condensates. In the latter system, the NLSE is known as the Gross-Pitaevskii equation [6].…”

mentioning

confidence: 99%

“…It is a universal model for nonlinear dispersive waves in many conservative physical systems including fluids [1,2], optical fibers [3], plasmas [4], magnetic spin waves [5], and Bose-Einstein condensates. In the latter system, the NLSE is known as the Gross-Pitaevskii equation [6].…”

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confidence: 99%

Linear and Nonlinear Bullets of the Bogoliubov–de Gennes Excitations

2017

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We report on the focalization of Bogoliubov-de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov-de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear "bullets"). These traveling Bogoliubov-de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice. DOI: 10.1103/PhysRevLett.118.044103 The nonlinear Schrödinger equation (NLSE) [5], and Bose-Einstein condensates. In the latter system, the NLSE is known as the Gross-Pitaevskii equation [6]. The NLSE, despite its apparent simplicity, supports a variety of fascinating nonlinear structures like solitons, breathers, recurrences, etc., hence being an attractive and rich model both in the description of natural phenomena and in technology-oriented research areas.In particular, the localized solutions of the NLSE and its generalizations have attracted considerable attention, and a huge amount of the scientific literature has been devoted to characterizing their existence and stability in various spatial dimensions.Written in a normalized form, the NLSE, for the temporal evolution of the field amplitude Aðr; tÞ defined in spacer and evolving in time t, readswhere c is the nonlinearity coefficient and ∇ 2 the Laplace operator.It is well known that the one-dimensional NLSE supports solitons in the strict mathematical sense, for focusing nonlinearity (c > 0). Zakharov and Shabat showed that a bright soliton solution exists [7]: In this case, the effects of nonlinear focusing and diffractive spreading are counterbalanced, and spatially localized nonlinear modes are stable. Bright solitons of the NLSE have been observed in nonlinear optics [8]. In fiber optics, solitons provide a powerful tool for optical communication systems [9].If a finite field background is present, coherent structures localized in space and in time, exhibiting periodic oscillations, the so-called breathers, have been predicted analytically [10][11][12] and observed experimentally [13]. Furthermore, new solutions on the finite background can be constructed by using refined mathematical techniques [14] showing the incredible richness of the NLSE.For c < 0, the NLSE is defocusing, and its homogeneous solution (the condensate) is stable. In this case, the NLSE supports the existence of vortices and dark or gray solitons [8] but not the bright soliton. Simply speaking, this is because both the diffraction and the nonlinearity tend to spread (defocus) the excitations over the homogeneous background. Ther...

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Dynamics of solitons in a domain wall in a ferromagnet

Cited by 26 publications

References 0 publications

Excitation of vortices using linear and nonlinear magnetostatic waves

Excitation of vortices using linear and nonlinear magnetostatic waves

Ginzburg-Landau model of Bose-Einstein condensation of magnons

Linear and Nonlinear Bullets of the Bogoliubov–de Gennes Excitations

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