Double sine-Gordon chain

Condat, C. A.; Guyer, R. A.; Miller, Michael David

doi:10.1103/physrevb.27.474

Cited by 117 publications

(78 citation statements)

References 18 publications

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“…Now we show that soliton complexes exist in the dispersive double sine-Gordon equations. These equations describe a large variety of physical systems: ferro-and antiferromagnets, magneto-elastic systems, superfluid 3 He and others [13]. Besides they contain dispersive sine-Gordon equations as the limit cases.…”

Section: Dispersive Models and Soliton-complex Solutionsmentioning

confidence: 99%

Formation of Soliton Complexes in Dispersive Systems

Bogdan¹,

Kosevich²,

Maugin³

1999

Condens. Matter Phys.

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The concept of soliton complex in a nonlinear dispersive medium is formulated. It is shown that interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its "excited" states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher order spatial or mixed derivatives. The dispersive sine-Gordon, double and triple sine-Gordon, and piecewise models are studied in detail. Mechanisms and conditions of the formation of soliton complexes, and peculiarities of their stationary dynamics are investigated. A phenomenological approach to the description of the complexes and the classification of all the possible complex states are proposed. Some examples of physical systems, where the phenomenon can be experimentally observed, are briefly discussed.

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Section: Dispersive Models and Soliton-complex Solutionsmentioning

confidence: 99%

Formation of Soliton Complexes in Dispersive Systems

Bogdan¹,

Kosevich²,

Maugin³

1999

Condens. Matter Phys.

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“…The double sine-Gordon potential (DSG) provides twokink solutions that can be used to model thick branes [7,[45][46][47][48][49]. Previous works have showed that splitting branes with internal structure, generated by two-kink defects, can foment the presence of resonant states [13][14][15].…”

Section: Double Sine-gordon Branementioning

confidence: 99%

Multiresonance modes in sine–Gordon brane models

et al. 2016

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In this work, we study the localization of the vector gauge field in two fivedimensional braneworlds generated by scalar fields coupled to gravity. The sine-Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sineGordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, where is concluded that the dilaton parameter regulates these corrections.

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“…(2.9) by examining the effective potential (2.10). We follow the idea described in [13], i.e., we find the minima of (2.10) since these determine the shape of the kink solutions of Eq. (2.1) (see [13] for further details).…”

Section: A Methods Of Averagingmentioning

confidence: 99%

“…We follow the idea described in [13], i.e., we find the minima of (2.10) since these determine the shape of the kink solutions of Eq. (2.1) (see [13] for further details). We assume that all the parameters are positive real numbers, i.e., α > 0, 1 > 0, 2 > 0, 3 > 0, and 1 > 2 .…”

Section: A Methods Of Averagingmentioning

confidence: 99%

Paramagnetic colloidal ribbons in a precessing magnetic field

et al. 2015

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We investigate the dynamics of a kink in a damped parametrically driven nonlinear Klein-Gordon equation. We show by using a method of averaging that, in the high-frequency limit, the kink moves in an effective potential and is driven by an effective constant force. We demonstrate that the shape of the solitary wave can be controlled via the frequency and the eccentricity of the modulation. This is in accordance with the experimental results reported in a recent paper [Casic et al., Phys. Rev. Lett. 110, 168302 (2013)], where the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a time-dependent magnetic field has been studied.

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Double sine-Gordon chain

Cited by 117 publications

References 18 publications

Formation of Soliton Complexes in Dispersive Systems

Formation of Soliton Complexes in Dispersive Systems

Multiresonance modes in sine–Gordon brane models

Paramagnetic colloidal ribbons in a precessing magnetic field

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