THE UNIFIED APPROACH TO INTEGRABLE RELATIVISTIC-EQUATIONS - SOLITON-SOLUTIONS OVER NONVANISHING BACKGROUNDS .1.

The scheme for unified description of integrable relativistic massive systems provides an inverse scattering formalism that encompasses univ ersally all (1+1)-dimensional systems of this kind. In this work the N -soliton solution (over an arbitrary background) is constructed for so me generic system which is associated with the s1(2, C) case of the sc heme and whose reductions include the complex sine-Gordon equation, th e massive Thirring model and other equations, both in the Euclidean an d Minkowski spaces. Thus the N-soliton solutions for all these systems emerge in a unified form differing only in the type of constraints im posed on their parameters. In an earlier paper the case of the zero ba ckground was considered, while here, we concentrate on the case of the nonvanishing constant background, i.e., on the N-kink solutions.