Connections between the soliton dynamics provided by some integrable relativistic theories.

The existence of soliton solutions is one of the main features of nonlinear wave models solvable by means of the inverse scattering method. Each of these models has associated a particular type of soliton; however, solitons always share a series of common properties: they behave as classical particles and their scattering processes may be interpreted as a succession of paired collisions in which every soliton collides with all others. In this way, the soliton dynamics provided by an integrable model can be formulated as a classical pure S-matrix theory. There are several relativistically invariant field theories in two-dimensiona1 space-time which can be solved through the inverse scattering method; therefore, it seems natural to investigate the correspondences among these relativistic models by considering their associated soliton dynamics. We have recently analyzed' the relationship between the massive Thirring (MT) and sineGordon (SG) models whose Lagrangian densities are