AKNS type reduced integrable bi-Hamiltonian hierarchies with four potentials

Abstract

The aim of this paper is to derive a kind of integrable hierarchies with four potentials, which possess bi-Hamiltonian structures, from reduced AKNS matrix spectral problems. The associated recursion operators are worked out explicitly. The Lax pair formulation and the trace identity are basic tools in the analysis. Two nonlinear examples in the resulting integrable hierarchies are integrable nonlinear Schrödinger type equations and integrable modified Korteweg–de Vries type equations.