AN ALGEBRAIC-METHOD TO CONSTRUCT THE DARBOUX MATRIX

We present an effective procedure to construct the I-soliton Darboux m atrix. Ou; approach, based on the Zakharov-Shabat-Mikhailov's dressing method, is especially useful in the case of non-canonical normalizati on and for non-isospectral linear problems. The construction is divide d into two steps. First, we represent a given linear problem as a syst em of some algebraic constraints on two matrices. In this context we i ntroduce and discuss invariants of the Darboux matrix. Second, we deri ve the Darboux matrix demanding that it preserves the algebraic constr aints. In particular, we consider in details the restrictions imposed by various reduction groups on the form of the Darboux matrix. (C) 199 5 American Institute of Physics.