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Quasi-Integrable Deformations of the Bullough-Dodd model

It has been shown recently that deformations of some integrable field theories in (1+1)-dimensions possess an infinite number of charges that are asymptotically conserved in the scattering of soliton like solutions. Such charges are not conserved in time and they do vary considerably during the scattering process, however they all return in the remote future (after the scattering) to the values they had in the remote past (before the scattering). Such non-linear phenomenon was named quasi-integrability, and it seems to be related to special properties of the solutions under a space-time parity transformation. In this paper we investigate, analytically and numerically, such phenomenon in the context of deformations of the integrable Bullough-Dodd model. We find that a special class of two-soliton like solutions of such deformed theories do present an infinite number of asymptotically conserved charges.