Abstract
We present a model of two-kinks resulting from an explicit composition of two standards kinks of the ϕ 4 model based on the procedure of ref. [1]. The two-kinks have an additional parameter accounting for the separation of the standard kinks of ϕ 4 model. We have shown that the two-kinks have two discrete internal modes besides the zeroth mode and the continuous spectrum. This new feature signalizes that the head-on collision a two-kinks/two-antikinks pair exhibits a rich and complex behavior due to the additional channel from which the energy of the system can be stored. We have exhibited the fractal structure associated with the main configurations after the collision. We have inferred the fractality as the imprint of the nonlinear exchange of energy into the two discrete internal modes.
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References
T. Uchiyama, Extended Hadron Model Based on the Modified sine-Gordon Equation, Phys. Rev. D 14 (1976) 3520 [INSPIRE].
D. Bazeia, J. Menezes and R. Menezes, New global defect structures, Phys. Rev. Lett. 91 (2003) 241601 [hep-th/0305234] [INSPIRE].
D. Bazeia, Defect structures in field theory, hep-th/0507188 [INSPIRE].
A.T. Avelar, D. Bazeia, L. Losano and R. Menezes, New Lump-like Structures in Scalar-field Models, Eur. Phys. J. C 55 (2008) 133 [arXiv:0711.4721] [INSPIRE].
A. Mukherjee, Some unusual classical lumps (1 + 1)-dimensions, Phys. Lett. B 151 (1985) 413 [INSPIRE].
D. Bazeia, C. Furtado and A.R. Gomes, Brane structure from scalar field in warped space-time, JCAP 02 (2004) 002 [hep-th/0308034] [INSPIRE].
A.E.R. Chumbes and M.B. Hott, Non-polynomial potentials with deformable topological structures, Phys. Rev. D 81 (2010) 045008 [arXiv:0905.4715] [INSPIRE].
A. de Souza Dutra, Continuously deformable topological structure, Physica D 238 (2009) 798.
M.A. Garcia-Nustes and J.A. Gonzalez, Formation of a two-kink soliton pair in perturbed sine-Gordon models due to kinkinternal-mode instabilities, Phys. Rev. E 86 (2012) 066602 [INSPIRE].
P.-O. Jubert, R. Allenspach and A. Bischof, Magnetic domain walls in constrained geometries, Phys. Rev. B 69 (2004) 220410 [cond-mat/0404669].
Duc-The Ngo, M.C. Hickey, S. McVitie, C.H. Marrows, J.N. Chapman and H. Awano, IEEE Trans. Magn. 47 (2011) 2511.
T.S. Mendonça and H.P. de Oliveira, The collision of two-kinks defects, arXiv:1502.03870 [INSPIRE].
H. Weigel, Kink-Antikink Scattering in φ 4 and ϕ 6 Models, J. Phys. Conf. Ser. 482 (2014) 012045 [arXiv:1309.6607] [INSPIRE].
A.M.H.H. Abdelhady, Scattering in Soliton Models and Crossing Symmetry, MSc Thesis, Stellenbosch University, Stellenbosch, South Africa (2012), unpublished.
M. Moshir, Soliton-Antisoliton Scattering and Capture in λϕ 4 Theory, Nucl. Phys. B 185 (1981) 318 [INSPIRE].
M.J. Ablowitz, M.D. Kruskal and J.F. Ladik, Solitary Wave Collisions, SIAM J. Appl. Math. 36 (1979) 428.
D.K. Campbell, J.F. Schonfeld and C.A. Wingate, Resonance structure in kink-antikink interactions in ϕ 4 theory, Physica D 9 (1983) 1.
D.K. Campbell and M. Peyrard, Solitary wave collisions revisited, Physica D 18 (1986) 47.
P. Anninos, S. Oliveira and R.A. Matzner, Fractal structure in the scalar λ(ϕ 2 − 1)2 theory, Phys. Rev. D 44 (1991) 1147 [INSPIRE].
R.H. Goodman and R. Haberman, Kink-Antikink Collisions in the ϕ 4 Equation: The n-Bounce Resonance and the Separatrix Map, SIAM J. Appl. Dyn. Syst. 4 (2005) 1195.
R.H. Goodman and R. Haberman, Chaotic Scattering and the n-Bounce Resonance in Solitary-Wave Interactions, Phys. Rev. Lett. 98 (2007) 104103.
P. Dorey, K. Mersh, T. Romanczukiewicz and Y. Shnir, Kink-antikink collisions in the ϕ 6 model, Phys. Rev. Lett. 107 (2011) 091602 [arXiv:1101.5951] [INSPIRE].
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ArXiv ePrint: 1504.07315
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Mendonça, T.S., de Oliveira, H.P. A note about a new class of two-kinks. J. High Energ. Phys. 2015, 133 (2015). https://doi.org/10.1007/JHEP06(2015)133
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DOI: https://doi.org/10.1007/JHEP06(2015)133