Structure and properties of four-kink multisolitons of the sine-Gordon equation

Gumerov, A. M.; Екомасов, Е. Г.; Zakir’yanov, F. K.; Kudryavtsev, R. V.

doi:10.1134/s0965542514030075

Cited by 16 publications

(13 citation statements)

References 31 publications

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“…We remark the impressive progress in scenarios with embedded topological defects, e.g., a skyrmion on a domain wall, or a Q-lump on a domain wall [3][4][5][6][7][8][9]. There are also interesting results on topological and non-topological solitons [10], multisoliton configurations [11,12], and on interaction of solitary waves with one another [13][14][15][16][17][18][19][20][21] and with impurities [22][23][24][25]. Various modifications of the Skyrme model have also been actively studied recently [26][27][28].…”

Section: Introductionmentioning

confidence: 87%

Scalar triplet on a domain wall: an exact solution

Gani¹,

Lizunova²,

Radomskiy³

2016

J. High Energ. Phys.

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We study a model with a real scalar Higgs field and a scalar triplet field that allows existence of a topological defect -- a domain wall. The wall breaks the global $O(3)$ symmetry of the model, which gives rise to non-Abelian orientational degrees of freedom. We found an exact analytic solution that describes a domain wall with a localized configuration of the triplet field on it. This solution enables one to calculate contributions to the action from the orientational and translational degrees of freedom of the triplet field. We also study the linear stability of the domain wall with the triplet field switched off. We obtain that degrees of freedom localized on the wall can appear or do not appear depending on the parameters of the model.Comment: 14 pages, 4 figures; v2: typos corrected, references added, minor changes to match version published in JHE

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Section: Introductionmentioning

confidence: 87%

Scalar triplet on a domain wall: an exact solution

Gani¹,

Lizunova²,

Radomskiy³

2016

J. High Energ. Phys.

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“…Today, the study of the properties of topological defects is a vast and very fast developing area. Interactions of kinks with each other and with impurities have been studied [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]; see also results for branes [44], bubble-like structures [45,46], interactions of breathers [47], and so on [48][49][50][51][52][53][54]. Many interesting and important results have been obtained in the (1+1)dimensional models with polynomial potentials: ϕ 4 , ϕ 6 , ϕ 8 , and so on [55][56][57][58][59][60][61][63][64][65][66][67][68][69][70]].…”

Section: Introductionmentioning

confidence: 99%

Scattering of the φ8 kinks with power-law asymptotics

Belendryasova

Gani

2019

Communications in Nonlinear Science and Numerical Simulation

104

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We study the scattering of the ϕ 8 kinks off each other, namely, we consider those ϕ 8 kinks that have power-law asymptotics. The slow power-law fall-off leads to a long-range interaction between the kink and the antikink. We investigate how the scattering scenarios depend on the initial velocities of the colliding kinks. In particular, we observe the 'escape windows' -the escape of the kinks after two or more collisions, explained by the resonant energy exchange between the translational and vibrational modes. In order to elucidate this phenomenon, we also analyze the excitation spectra of a solitary kink and of a composite kink+antikink configuration.

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“…A soliton in a translationally invariant model can always be shifted by a constant vector, which means that there always exists the zero (translational) mode. Excitations with higher energies -vibrational modes -can give rise to a rich collection of resonance phenomena in kink-(anti)kink collisions, as well as in the scattering of kinks off impurities [24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Kink excitation spectra in the (1+1)-dimensional φ8 model

Gani

Lensky

Lizunova

2015

J. High Energ. Phys.

114

110

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Abstract:We study excitation spectra of BPS-saturated topological solutions -the kinks -of the ϕ 8 scalar field model in (1 + 1) dimensions, for three different choices of the model parameters. We demonstrate that some of these kinks have a vibrational mode, apart from the trivial zero (translational) excitation. One of the considered kinks is shown to have three vibrational modes. We perform a numerical calculation of the kink-kink scattering in one of the considered variants of the ϕ 8 model, and find the critical collision velocity v cr that separates the different collision regimes: inelastic bounce of the kinks at v in ≥ v cr , and capture at v in < v cr . We also observe escape windows at some values of v in < v cr where the kinks escape to infinity after bouncing off each other two or more times. We analyse the features of these windows and discuss their relation to the resonant energy exchange between the translational and the vibrational excitations of the colliding kinks.

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Structure and properties of four-kink multisolitons of the sine-Gordon equation

Cited by 16 publications

References 31 publications

Scalar triplet on a domain wall: an exact solution

Scalar triplet on a domain wall: an exact solution

Scattering of the φ8 kinks with power-law asymptotics

Kink excitation spectra in the (1+1)-dimensional φ8 model

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