An integrable generalization of the Kaup–Newell soliton hierarchy

Abstract

A generalization of the Kaup–Newell spectral problem associated with sl is introduced and the corresponding generalized Kaup–Newell hierarchy of soliton equations is generated. Bi-Hamiltonian structures of the resulting soliton hierarchy, leading to a common recursion operator, are furnished by using the trace identity, and thus, the Liouville integrability is shown for all systems in the new generalized soliton hierarchy. The involved bi-Hamiltonian property is explored by using the computer algebra system Maple.