Kink-antikink interactions in the double sine-Gordon equation

Campbell, David; Peyrard, Michel; Sodano, P.

doi:10.1016/0167-2789(86)90019-9

Cited by 308 publications

(279 citation statements)

References 22 publications

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“…His clear that the procedure we have worked out to obtain the mean kink parameters is quite general, and likely to apply to a number of different soli ton-bearing systems, such as those we mentioned in the Introduction (<jJ4 [18], double SG [19], generalized SG [20]). The reason is that they also allow for kink propagation and the collective-coordinate approximation is as good as in the SG equation; then, the single-scatterer effective potential can be computed and the formalism we present here applies inmediately.…”

Section: Discussionmentioning

confidence: 99%

“…To deal with the soobtained equation, we elaborate a statistical method to compute directly the mean values of the kink parameters. This procedure is rather general, and it may be useful in other similar problems, such as, e.g., propagation ofkinks along spatially disordered rp4 [18], double-SG (19], or generalized-SG [20] models, as well as for other nonlinear systems supporting topological. kinks.…”

mentioning

confidence: 99%

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Kink propagation through disordered media

Gredeskul¹,

Kivshar²,

Maslov³

et al. 1992

Phys. Rev. A

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Kink propagation through disordered media

Gredeskul¹,

Kivshar²,

Maslov³

et al. 1992

Phys. Rev. A

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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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“…A merger of a colliding kink and antikink into a breather is possible in a nonintegrable system when energy loss to radiation and/or excitation of the kink's internal modes is sufficiently large [58][59][60][61]. The binding of a free kink and antikink into a breather has been addressed in [62] in the presence of spatially periodic perturbation.…”

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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Kink-antikink interactions in the double sine-Gordon equation

Cited by 308 publications

References 22 publications

Kink propagation through disordered media

Kink propagation through disordered media

Multiresonance modes in sine–Gordon brane models

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

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