On classification of soliton solutions of multicomponent nonlinear evolution equations.

We consider several ways of how one could classify the various types of soliton solutions related to multicomponent nonlinear evolution equations which are solvable by the inverse scattering method for the generalized Zakharov-Shabat system related to a simple Lie algebra g. In doing so we make use of the fundamental analytic solutions, the Zakharov-Shabat dressing procedure, the reduction technique and other tools characteristic for that method. The multicomponent solitons are characterized by several important factors: the subalgebras of g and the way these subalgebras are embedded in g, the dimension of the corresponding eigensubspaces of the Lax operator L, as well as by additional constraints imposed by reductions. [ABSTRACT FROM AUTHOR]