A (2+1)-DIMENSIONAL SINE-GORDON SYSTEM - ITS AUTO-BACKLUND TRANSFORMATION

An integrable (2+1)-dimensional sine-Gordon equation wherein the spatial variables occur in a symmetric manner was recently introduced by Konopelchenko and Rogers. It represents a (2+1)-dimensional extension of the classical sine-Gordon equation analogous to the Nizhnik-Novikov-Veselov generalization of the Korteweg-de Vries equation and the Davey-Stewartson generalization of the nonlinear Schrodinger equation. Here, an auto-Backlund transformation is constructed via a generalized Darboux-Levi approach both for the (2+1)-dimensional sine-Gordon equation and an integrable coupled system in which it is embedded. An iterated version of the auto-Backlund transformation is presented along with a class of exact solutions.