Sine-gordon wobbles through bäcklund transformations

Abstract

In this work we construct the wobble exact solution of sine-Gordon equation by means of Bäcklund Transformations. We find the parameters of the transformations corresponding to the Bianchi diagram for the wobble as a particular 3-soliton solutions. We show that this solution agrees with the wobbles obtained by Kälbermann and Segur by means of the Inverse Scattering Transform, and by Ferreira et al. using the Hirota method. The new formulation introduced allows to identify easily the parameters that de fine the building blocks of this solution { a kink and a breather, and can be used in further studies of this solution in the perturbed sine-Gordon equation.