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The concept of quasi-integrability: a concrete example

Ferreira, Luiz Agostinho; Zakrzewski, Wojtek J. Universidade De São Paulo

JOURNAL OF HIGH ENERGY PHYSICS, n.5, 2011

SPRINGER 2011

Acesso online

  • Título:
    The concept of quasi-integrability: a concrete example
  • Autor: Ferreira, Luiz Agostinho; Zakrzewski, Wojtek J.
  • Universidade De São Paulo
  • Assuntos: Integrable Field Theories; Integrable Equations In Physics; Solitons Monopoles And Instantons; Integrable Hierarchies; Zero-Curvature Conditions; Sine-Gordon Equation; Duality; Waves; Physics; Particles & Fields
  • É parte de: JOURNAL OF HIGH ENERGY PHYSICS, n.5, 2011
  • Descrição: We use the deformed sine-Gordon models recently presented by Bazeia et al [1] to take the first steps towards defining the concept of quasi-integrability. We consider one such definition and use it to calculate an infinite number of quasi-conserved quantities through a modification of the usual techniques of integrable field theories. Performing an expansion around the sine-Gordon theory we are able to evaluate the charges and the anomalies of their conservation laws in a perturbative power series in a small parameter which describes the ""closeness"" to the integrable sine-Gordon model. We show that in the case of the two-soliton scattering the charges, up to first order of perturbation, are conserved asymptotically, i.e. their values are the same in the distant past and future, when the solitons are well separated. We indicate that this property may hold or not to higher orders depending on the behavior of the two-soliton solution under a special parity transformation. For closely bound systems, such as breather-like field configurations, the situation however is more complex and perhaps the anomalies have a different structure implying that the concept of quasi-integrability does not apply in the same way as in the scattering of solitons. We back up our results with the data of many numerical simulations which also demonstrate the existence of long lived breather-like and wobble-like states in these models.
    Royal Society
    CNPq
    FAPESP
  • DOI: 10.1007/JHEP05(2011)130
  • Títulos relacionados: Journal of High Energy Physics
  • Editor: SPRINGER
  • Data de publicação: 2011
  • Idioma: Inglês

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