Abstract
Following our attempts to define quasi-integrability in which we related this concept to a particular symmetry of the two-soliton function we check this condition in three classes of modified sine-Gordon models in (1 + 1) dimensions. We find that the numerical results seen in various scatterings of two solitons and in the time evolution of breather-like structures support our ideas about the symmetry of the field configurations and its effects on the anomalies of the conservation laws of the charges.
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L. Ferreira and W.J. Zakrzewski, The concept of quasi-integrability: a concrete example, JHEP 05 (2011) 130 [arXiv:1011.2176] [INSPIRE].
L. Ferreira, G. Luchini and W.J. Zakrzewski, The concept of quasi-integrability for modified non-linear Schrödinger models, JHEP 09 (2012) 103 [arXiv:1206.5808] [INSPIRE].
J. Hietarinta, Hirota’s bilinear method and partial integrability, in Partially Integrable Evolution Equations in Physics, R. Conte and N. Boccara eds., NATO ASI Series C 310, Les Houches France March 21-30 1989 [INSPIRE].
T. Kuusela and J. Hietarinta, Elastic scattering of solitary waves in the strongly dissipative Toda lattice, Phys. Rev. Lett. 62 (1989) 700.
D. Bazeia, L. Losano, J. Malbouisson and R. Menezes, Classical behavior of deformed sine-Gordon models, Physica D 237 (2008) 937 [arXiv:0708.1740] [INSPIRE].
C. Adam, L. Ferreira, E. da Hora, A. Wereszczynski and W. Zakrzewski, Some aspects of self-duality and generalised BPS theories, JHEP 08 (2013) 062 [arXiv:1305.7239] [INSPIRE].
L. Ferreira and W.J. Zakrzewski, A simple formula for the conserved charges of soliton theories, JHEP 09 (2007) 015 [arXiv:0707.1603] [INSPIRE].
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ArXiv ePrint: 1308.4412
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Ferreira, L.A., Zakrzewski, W.J. Numerical and analytical tests of quasi-integrability in modified sine-Gordon models. J. High Energ. Phys. 2014, 58 (2014). https://doi.org/10.1007/JHEP01(2014)058
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DOI: https://doi.org/10.1007/JHEP01(2014)058