The concept of quasi-integrability: a concrete example

Details The concept of quasi-integrability: a concrete example The concept of quasi-integrability: a concrete example

2010-11-09

arxiv.org/abs/1011.2176v1

JHEP 1105:130,2011

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, 47 ps figures

Scientific paper

10.1007/JHEP05(2011)130

We use the deformed sine-Gordon models recently presented by Bazeia et al to discuss possible definitions of quasi-integrability. We present 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. Our results indicate that in the case of the two-soliton scattering the charges are conserved asymptotically, i.e. their values are the same in the distant past and future, when the solitons are well separated. We back up our results with numerical simulations which also demonstrate the existence of long lived breather-like and wobble-like states in these models.

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