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The perturbed sine - Gordon soliton solutions (kinks, breathers) in laboratory coordinates are derived by a Green function formalism in a novel way dispensing with any inverse scattering methods. Besides the Bäcklund transformation, a simple approach based on Green's theorem is employed for determining the Green functions. A systematic treatment allows the adiabatic approximation to be derived in a new manner. The results are compared to those of the relevant papers in this field and thereby further insight is provided. In a simple example (a kink scattered by an impurity) the calculation of energy radiation is demonstrated.
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E. Mann (1997) studied this question.
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