Soliton hierarchies from matrix loop algebras

Abstract

Matrix loop algebras, both semisimple and non-semisimple, are used to generate soliton hierarchies. Hamiltonian structures to guarantee the Liouville integrability are determined by using the trace identity or the variational identity. An application example is presented from a perturbed Kaup–Newell matrix spectral problem associated with the three-dimensional real special linear algebra.