Sine-Gordon wobbles through bäcklund transformations

In this work we construct the wobble exact solution of sine-Gordon equation by means of B acklund Transformations. We nd 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 K albermann 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 ne 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.We acknowledge nancial support from MICINN through grants MOSAICO (SC, AS) and FIS2008-02380/FIS (NRQ), and grants FQM207 and P06-FQM-01735 (NRQ) (from Junta de Andalucía, Spain), and SIMUMAT-CM (AS) (from Comunidad de Madrid, Spain).Publicad