Scalar Lax-pairs and soliton solutions of the generalized periodic Toda lattice

Abstract

In this chapter we suggest a general scheme for constructing solitons of dynamical systems without referring to the matrix realization of the Lax-type representation. In the ISP method, which helps one find the soliton-type solutions are found, a lucky choice of an LA-pair facilitates the calculations considerably and, moreover, in principle enables one to perform them. The approach suggested in what follows is invariant with respect to a concrete representation of the algebra of internal symmetries and appeals directly to the properties of the algebra.