Wobbling double sine-Gordon kinks

Campos, João G. F.; Mohammadi, Azadeh

doi:10.1007/jhep09(2021)067

Cited by 27 publications

(14 citation statements)

References 63 publications

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“…The sine-Gordon system is important because it is the only integrable Klein-Gordon kinkbearing system which yields soliton solutions. The double SG (DSG) model which is a modified version of the SG model has also received much attention [32][33][34][35][36]. Interestingly, the DSG system is used for the description of some physical systems such as gold dislocations [37], optical pulses [38], and Josephson structures [39].…”

Section: Introductionmentioning

confidence: 99%

Scattering of kinks in the $Bφ^{4}$ model

Mohammadi¹,

Momeni²

2022

Preprint

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In this study, based on the ϕ 4 model, a new model (called the Bϕ 4 model) is introduced in which the potential form for the values of the field whose magnitudes are greater than 1 is multiplied by the positive number B. All features related to a single kink (antikink) solution remain unchanged and are independent of parameter B. However, when a kink interacts with an antikink in a collision, the results will significantly depend on parameter B. Hence, for kink-antikink collisions, many features such as the critical speed, output velocities for a fixed initial speed, two-bounce scattering windows, extreme values, and fractal structure in terms of parameter B are considered in detail numerically. The role of parameter B in the emergence of a nearly soliton behavior in kink-antikink collisions at some initial speed intervals is clearly confirmed. The fractal structure in the diagrams of scattering windows is seen for the regime B ≤ 1. However, for the regime B > 1, this behavior gradually becomes fuzzing and chaotic as it approaches B = 3.3. The case B = 3.3 is obtained again as the minimum of the critical speed curve as a function of B. For the regime 3.3 < B ≤ 10, the chaotic behavior gradually decreases. However, a fractal structure is never observed. Nevertheless, it is shown that despite the fuzzing and shuffling of the scattering windows, they follow the rules of the resonant energy exchange theory.

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Section: Introductionmentioning

confidence: 99%

Scattering of kinks in the $Bφ^{4}$ model

Mohammadi¹,

Momeni²

2022

Preprint

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“…For that reason kinks interaction in higher order models is more interesting and some phenomenons like resonant scattering structure, escape windows [47][48][49] or even the extreme values of the energy densities [50] depend on the order in which kinks collide. Many important results have also been obtained for topological field configurations in [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]. Consequently, it is important to know how an asymmetric φ 6 kink treats when it interacts with a PT -symmetric perturbation.…”

Section: Introductionmentioning

confidence: 99%

Scattering of the asymmetric $ϕ^6$ kinks from a $\mathcal{PT}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons

Saadatmand,

Marjaneh

2022

Preprint

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Interaction of asymmetric φ 6 kinks with a spatially localized PT -symmetric perturbation is investigated numerically. It has been shown that when the kink (antikink) hits the defect from the gain side, a final velocity of the kink decreases (increases), while for the kink and antikink coming from the opposite direction their final velocities remain unchanged. It is also found that when the kink interacts with the defect from the gain side multiple pair of the kink-antikink are formed from small amplitude waves (phonons) in the final states depending on the initial velocity of the initial kink and parameter of the perturbation.

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“…In the same context, Barashenkov and Oxtoby [72] employ a singular perturbation expansion which remains uniform to all orders by introducing a hierarchy of space and times scales. Furthermore, the collision between wobbling kinks has been investigated in the φ 4 -model [74,75] and the double sine-Gordon model [76].…”

Section: Introductionmentioning

confidence: 99%

Wobbling kinks in a two-component scalar field theory: Interaction between shape modes

Alonso-Izquierdo¹,

Miguélez-Caballero²,

Nieto³

et al. 2022

Preprint

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In this paper the interaction between the shape modes of the wobbling kinks arising in the family of two-component MSTB scalar field theory models is studied. The spectrum of the second order small kink fluctuation in this model has two localized vibrational modes associated to longitudinal and orthogonal fluctuations with respect to the kink orbit. It has been found that the excitation of the orthogonal shape mode immediately triggers the longitudinal one. In the first component channel the kink emits radiation with twice the orthogonal wobbling frequency (not the longitudinal one as happens in the φ 4 -model). The radiation emitted in the second component has two dominant frequencies: one is three times the frequency of the orthogonal wobbling mode and the other is the sum of the frequencies of the longitudinal and orthogonal vibration modes. This feature is explained analytically using perturbation expansion theories.

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Wobbling double sine-Gordon kinks

Cited by 27 publications

References 63 publications

Scattering of kinks in the $Bφ^{4}$ model

Scattering of kinks in the $Bφ^{4}$ model

Scattering of the asymmetric $ϕ^6$ kinks from a $\mathcal{PT}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons

Wobbling kinks in a two-component scalar field theory: Interaction between shape modes

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