Classical matrix sine-Gordon theory

Abstract

The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the A3 generalization where fields take values in SU(2) describes integrable deformations of conformal field theory corresponding to the coset SU(2) × SU(2)/SU(2). Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and breathers which generalize 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 Backlund 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 principle by making use of Bianchi's permutability theorem.