Moving Embedded Solitons in the Discrete Double Sine-Gordon Equation

Zolotaryuk, Yaroslav; Starodub, Ivan O.

doi:10.1007/978-3-319-72218-4_13

Cited by 4 publications

(6 citation statements)

References 53 publications

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“…The A(s) behaviour for this lattice is different from the analogous figure for the discrete Klein-Gordon lattice with harmonic interactions 51 , where the dependence A(s) is generally single valued.…”

Section: Obtention Of Travelling Nanopterons and Kinks Withmentioning

confidence: 56%

Nonlinear waves in a model for silicate layers

Archilla

Zolotaryuk

Kosevich

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggests that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based on physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work, we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions, and bi-crowdions. We analyze their velocities, energies, and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.

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Section: Obtention Of Travelling Nanopterons and Kinks Withmentioning

confidence: 56%

Nonlinear waves in a model for silicate layers

Archilla

Zolotaryuk

Kosevich

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…propagating in nonlinear chains with selected velocities have been reported in a number of studies, e.g., in Refs. [67][68][69][70][71][72][73]. Similarly, the crowdion inverse width β monotonically increases for 0 < v 0 < 5, but it has discrete values for faster crowdions.…”

Section: Moving Crowdionsmentioning

confidence: 93%

Mass transfer in the Frenkel-Kontorova chain initiated by molecule impact

et al. 2018

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“…It can be proved [42,43] that static kinks of the model (7) can be derived iteratively from the two-point map of setting (9) equal to 0, which is quadratic algebraic equation having the roots…”

Section: B Exceptional Discretization Of the φ 4 Equationmentioning

confidence: 99%

“…Let φ 0 n be an equilibrium static solution of Eq. (7). Small-amplitude oscillations around this solution can be studied by inserting φ n (t) = φ 0 n + ε n (t) into the equation of motion (7), where ε n ≪ 1, and obtaining the linearized equation in the form…”

Section: Spectrum Of Vacuum and Small-amplitude Vibrations Localizmentioning

confidence: 99%

“…[2][3][4][5][6]. The case of strong discreteness is of particular interest and it is encountered in many applications, for example, in the description of arrays of Josephson junctions [7], dissipative nonlinear discrete systems [8], dynamics of crowdions [9][10][11][12][13] and dislocations [14][15][16] in crystals, propagation of domain walls in magnetic materials [17], motion of spring-mass chains [18], in the discussion of electric charge transport in molecular chains [19]. The consideration of the strongly discrete (anti-continuum) limit is a well-known approach aiming towards the analytical treatment of discrete breathers [20,21].…”

Section: Introductionmentioning

confidence: 99%

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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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Moving Embedded Solitons in the Discrete Double Sine-Gordon Equation

Cited by 4 publications

References 53 publications

Nonlinear waves in a model for silicate layers

Nonlinear waves in a model for silicate layers

Mass transfer in the Frenkel-Kontorova chain initiated by molecule impact

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