Dressing Chain Equations Associated to Difference Soliton Systems

Links of factorization theory, supersymmetry and Darboux transformations as isospectral deformations of difference operators are considered in the context of soliton theory. The dressing chain equations for factorizing operators of a spectral problem are derived. The chain equations itselves yield nonlinear systems which closure generates solutions of the equations as well as of the nonlinear system if both operators of the correspondent Hirota bilinearization are covariant with respect to Darboux transformation which hence defines a symmetry of the nonlinear system as well as of these closed chains. Examples of Hirota and Nahm equations are specified.