A soliton hierarchy derived from a fourth-order matrix spectral problem possessing four fields

Abstract

This paper is dedicated to the construction of integrable commuting flows starting from a fourth-order matrix spectral problem involving four fields, which is derived from a specialized matrix Lie algebra over the real domain. This work includes the development of an explicit bi-Hamiltonian formulation and a hereditary recursion structure, which confirms the hierarchy’s integrability in the Liouville sense. Furthermore, we examine two second-order and third-order integrable models, along with their reduced, uncombined forms.