Fractal structures and multiparticle effects in soliton scattering

Kivshar, Yuri S.; Shigenari, Takeshi

doi:10.1103/physreve.64.056613

Cited by 44 publications

(51 citation statements)

References 16 publications

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“…In particular, the kink-(anti)kink scattering and the interactions of kinks with impurities are of growing interest. A wide variety of phenomena emerges in these systems, e.g., escape windows and quasi-resonances in kink-(antikink) collisions [20][21][22][23][24][25][26][27][28][29][30], resonant interactions of kinks with wells, barriers and impurities [31][32][33][34], non-radiative energy exchange in multi-soliton collisions [35][36][37]. It is interesting that the presence of a kink's internal modes does not guarantee the appearance of resonance windows, as it has been recently shown for the deformed φ 4 model [38].…”

Section: Introductionmentioning

confidence: 99%

Multi-kink collisions in the ϕ 6 model

Marjaneh

Gani

Saadatmand

et al. 2017

J. High Energ. Phys.

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We study simultaneous collisions of two, three, and four kinks and antikinks of the φ 6 model at the same spatial point. Unlike the φ 4 kinks, the φ 6 kinks are asymmetric and this enriches the variety of the collision scenarios. In our numerical simulations we observe both reflection and bound state formation depending on the number of kinks and on their spatial ordering in the initial configuration. We also analyze the extreme values of the energy densities and the field gradient observed during the collisions. Our results suggest that very high energy densities can be produced in multi-kink collisions in a controllable manner. Appearance of high energy density spots in multi-kink collisions can be important in various physical applications of the Klein-Gordon model.

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Section: Introductionmentioning

confidence: 99%

Multi-kink collisions in the ϕ 6 model

Marjaneh

Gani

Saadatmand

et al. 2017

J. High Energ. Phys.

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“…Interaction of solitary waves with each other [46][47][48] and with local inhomogeneities of media has been attracting the attention of researchers for the past two decades. Interaction of a fluxon with a localized inhomogeneity in a long Josephson junction has been investigated in [49,50].…”

Section: Introductionmentioning

confidence: 99%

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect

2014

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The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.

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“…[11][12][13][14][15] и список литературы в этих работах). Обычно в данных исследованиях обсуждается степень неупруго-сти солитонных столкновений, зависимость результата столкновения от разности фаз солитонов, фрактальное рассеяние солитонов.…”

Section: Introductionunclassified

Soliton collision in discrete PT-symmetric systems without Peierls-Nabarro potential

Suchkov¹,

Khare²

2011

LoM

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Рассматривается дискретная модель, описывающая си-стему волноводов с притоком и оттоком энергии, допу-скающая точные решения в виде волн солитонного типа. Показано существование солитонов двух типов -высо-кочастотного и низкочастотного и исследована дина-мика взаимодействия солитонов как одного типа, так и разных типов. Установлено, что солитоны одного типа взаимодействуют абсолютно упруго, в то время как ре-зультат взаимодействия солитонов разного типа суще-ственно зависит от начальных условий.Ключевые слова: PT -симметричные системы, солитон, PT -симметричный каплер, нелинейное уравнение Шрединге-ра, потенциал Паейрлса-Набарро.Discrete model describing a waveguide array with energy gain and loss that admits exact solitary wave solutions was considered. Existence of two types of solitons, namely, the high-frequency and the low-frequency ones was demonstrated. Collisions between similar and dissimilar solitons were investigated. It was found that solitons of the same type interact elastically, while for dissimilar solitons the collision outcome significantly depends on the initial conditions.

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Fractal structures and multiparticle effects in soliton scattering

Cited by 44 publications

References 16 publications

Multi-kink collisions in the ϕ 6 model

Multi-kink collisions in the ϕ 6 model

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect

Soliton collision in discrete PT-symmetric systems without Peierls-Nabarro potential

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