A coupled AKNS–Kaup–Newell soliton hierarchy

A coupled AKNS–Kaup–Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS–Kaup–Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of the systems lead to the AKNS hierarchy and the Kaup–Newell hierarchy, and thus those two soliton hierarchies also possess tri-Hamiltonian structures.

[1]  A. Fordy,et al.  Coupled KdV equations with multi-Hamiltonian structures , 1987 .

[2]  Athanassios S. Fokas,et al.  Symplectic structures, their B?acklund transformation and hereditary symmetries , 1981 .

[3]  Extending Hamiltonian operators to get bi-Hamiltonian coupled KdV systems , 1998, solv-int/9807002.

[4]  Ruguang Zhou,et al.  LETTER TO THE EDITOR: On inverse recursion operator and tri-Hamiltonian formulation for a Kaup-Newell system of DNLS equations , 1999 .

[5]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[6]  P. Caudrey,et al.  A hierarchy of Hamiltonian evolution equations associated with a generalized Schrödinger spectral problem , 1984 .

[7]  G. Soliani,et al.  Nonlinear Evolution Equations and Dynamical Systems , 1980 .

[8]  A. Fokas,et al.  The hierarchy of the Benjamin-Ono equation , 1981 .

[9]  Franco Magri,et al.  A Simple model of the integrable Hamiltonian equation , 1978 .

[10]  Allan P. Fordy,et al.  Coupled Harry Dym equations with multi-Hamiltonian structures , 1988 .

[11]  Wen-Xiu Ma,et al.  An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems , 1994 .

[12]  Wen-Xiu Ma,et al.  A hierarchy of coupled Burgers systems possessing a hereditary structure , 1993 .

[13]  Alan C. Newell,et al.  Solitons in mathematics and physics , 1987 .

[14]  Binary non-linearization of Lax pairs of Kaup-Newell soliton hierarchy , 1996, solv-int/9608003.

[15]  Wen-Xiu Ma,et al.  THE BI-HAMILTONIAN STRUCTURE OF THE PERTURBATION EQUATIONS OF THE KDV HIERARCHY , 1996 .

[16]  W. Ma.  A CLASS OF COUPLED KDV SYSTEMS AND THEIR BI-HAMILTONIAN FORMULATION , 1998, solv-int/9803009.

[17]  I. Gel'fand,et al.  Hamiltonian operators and algebraic structures related to them , 1979 .