Perturbation-induced evolution of a soliton–antisoliton pair in the sine-Gordon system

The evolution of a soliton–antisoliton solution of the perturbed sine-Gordon equation is studied, using a perturbation theory for solitons which is based on the inverse scattering method. The following processes are described within the adiabatic approximation: soliton and antisoliton annihilation under the action of friction with the formation of a bound state, a bion; generation of a quasibound soliton–antisoliton pair in an external constant field; and the effect of an external field on soliton–antisoliton scattering in a dissipative system. The nature of these processes depends substantially on the initial parameter values of the colliding solitary waves. To first approximation, the perturbation is shown to generate no new soliton–antisoliton pairs and bions, thus making it possible to confine the analysis to the adiabatic approximation only.

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