CLASSICAL MATRIX SINE-GORDON THEORY

The matrix sine-Gordon theory, a matrix generalization of the well-kno wn sine-Gordon theory, is studied. In particular, the A(3) generalizat ion where fields take values in SU(2) describes integrable deformation s of conformal field theory corresponding to the coset SU(2) x SU(2)/S U(2). Various classical aspects of the matrix sine-Gordon theory are a ddressed. We find exact solutions, solitons and breathers which genera lize those of the sine-Gordon theory with internal degrees of freedom, by applying the Zakharov-Shabat dressing method and explaining their physical properties. Infinite current conservation laws and then Backl und transformation of the theory are obtained from the zero curvature formalism of the equation of motion. From the Backlund transformation, we also derive exact solutions as well as a nonlinear superposition p rinciple by making use of Bianchi's permutability theorem.