Breather-like structures in modified sine-Gordon models

Abstract

We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1 + 1) dimensions. The main motivation of our study is to test the ideas behind the recently proposed concept of quasi-integrability, which emerged from the observation that some field theories possess an infinite number of quantities which are asymptotically conserved in the scattering of solitons, and periodic in time in the case of breather-like configurations. Even though the mechanism responsible for such phenomena is not well understood yet, it is clear that special properties of the solutions under a space-time parity transformation play a crucial role. The numerical results of the present paper give support for the ideas on quasi-integrability, as it is found that extremely long-lived breather configurations satisfy these parity properties. We also report on a mechanism, particular to the theory studied here, that favours the existence of long lived breathers even in cases of significant deformations of the sine-Gordon potential. We also find numerically that our breather-like configurations decay through the gradual increase of their frequency of oscillations.