An integrable generalization of the Kaup-Newell soliton hierarchy

Abstract

A generalization of the Kaup-Newell spectral problem associated with sl (2, ℝ) 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. © 2013 Sociedad Española de Oftalmología. Published by Elsevier España, S.L. All rightsreserved.