Interaction of sine‐Gordon solitons in the model with attracting impurities

Екомасов, Е. Г.; Gumerov, A. M.; Муртазин, Р. Р.

doi:10.1002/mma.3908

Cited by 9 publications

(7 citation statements)

References 34 publications

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“…However, the dependences obtained are very far from the breather amplitude of the model (2.3). It was calculated by the numerical method described in [21]. Nevertheless, the nature of the dependences is qualitatively the same: one maximum is present in all the curves in Fig.…”

Section: Nondissipative Casementioning

confidence: 89%

“…The effect of small perturbations on the SGE solutions can be studied using a well-developed perturbation theory for solitons [5,19,20]. The effect of perturbations can generally be investigated only with the help of numerical methods [20][21][22][23]. For example, the influence of a coordinate-and time-dependent external force has been studied [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…The importance of impurity modes in the kink dynamics was shown in [5,28,36]. The structure and properties of localized nonlinear waves excited on an impurity were analyzed numerically in [21,23,32]. The case of several point impurities that are of interest in some physical applications was considered in [44] and even the case of spatially modulated harmonic potential was considered [31].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Nondissipative Casementioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…This leads to substantial changes in the structure and energy of solitons. The (3+1)-(2+1)-dimensional models are often studied (e. g., [5][6][7][8][9]). However, the (1+1)-dimensional models are the most studied.…”

Section: Introductionmentioning

confidence: 99%

Changing the Dynamic Parameters of Localized Breather and Soliton Waves in the Sine-Gordon Model with Extended Impurity, External Force, and Decay in the Autoresonance Mode

Екомасов¹,

Назаров²,

Samsonov³

2022

Nelin. Dinam.

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Possibility of changing the dynamic parameters of localized breather and soliton waves for the sine-Gordon equation in the model with extended impurity, variable external force and dissipation was investigated using the autoresonance method. The model of ferromagnetic structure consisting of two wide identical layers separated by a thin layer with modified values of magnetic anisotropy parameter was taken as a basis. Frequency of external field is a linear function of time. The sine-Gordon equation (SGE) was solved numerically using the finite differences method with explicit scheme of integration. For certain values of the extended impurity parameters a magnetic inhomogeneity in the form of magnetic breather is formed when domain wall passes through it with constant velocity. The numerical simulation showed that using special variable force and small amplitude it is possible to resonantly increase the amplitude of breather. For each case of the impurity parameters values, there is a threshold value of the magnetic field amplitude leading to resonance. Geometric parameters of thin layer also have influence on the resonance effect — for decreasing layer width the breather amplitude grows more slowly. For large layer width the translation mode of breather oscillations is also excited. For certain parameters of extended impurity, a soliton can form. For a special type of variable field with frequency linearly dependent on time, soliton is switched to antisoliton and vice versa.

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“…One particularly central problem in the dynamics of solitary waves is the analysis of their collision outcomes, especially beyond the merely-phase-shifting elastic wave interactions within integrable models [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Continuum Klein-Gordon equations, apart from the famous integrable sine-Gordon example [4], support exact solutions in the form of moving kinks which interact inelastically.…”

Section: Introductionmentioning

confidence: 99%

Fischer Tropsch Synthesis: The Promoter Effects, Operating Conditions, and Reactor SynthesisThe authors gratefully acknowledge University of Sistan and Baluchestan for helping and supporting this research.Majid Sarkari:Young Researchers Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran. Farhad Fazlollahi: Department of Chemical Engineering, Science and Research Branch, Islamic Azad University, Fars, Iran. Hossein Atashi: Department of Chemical Engineering, Faculty of Engineering, University of Sis

Sarkari¹,

Fazlollahi²,

Atashi³

2018

Energyo

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The two major effects observed in collisions of the continuum φ 4 kinks are (i) the existence of critical collision velocity v c above which the kinks always emerge from the collision and (ii) the existence of the escape windows for multi-bounce collisions with the velocity below v c , associated with the energy exchange between the kink's internal and translational modes. The potential merger (for sufficiently low collision speeds) of the kink and antikink produces a bion with oscillation frequency ω B , which constantly radiates energy, since its higher harmonics are always within the phonon spectrum. Similar effects have been observed in the discrete φ 4 kink-antikink collisions for relatively weak discreteness. Here we analyze kink-antikink collisions in the regime of strong discreteness considering an exceptional discretization of the φ 4 field equation where the static Peierls-Nabarro potential is precisely zero and the not-too-fast kinks can propagate practically radiating no energy. Several new effects are observed in this case, originating from the fact that the phonon band width is small for strongly discrete lattices and for even higher discreteness an inversion of the phonon spectrum takes place with the short waves becoming low-frequency waves.When the phonon band is narrow, not a bion but a discrete breather with frequency ω DB and all higher harmonics being outside the phonon band is formed. When the phonon spectrum is inverted, the kink and antikink become mutually repulsive solitary waves with oscillatory tails, and their collision is possible only for velocities above a threshold value sufficient to overcome their repulsion.

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Interaction of sine‐Gordon solitons in the model with attracting impurities

Cited by 9 publications

References 34 publications

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

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

Changing the Dynamic Parameters of Localized Breather and Soliton Waves in the Sine-Gordon Model with Extended Impurity, External Force, and Decay in the Autoresonance Mode

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