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.Comment: 15 pages, late

Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitrary purely imaginary Riemann matrix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinear forms: $u_t+u_{xxy}-3uu_y-3u_xv=0$ and $u_t+u_{xxxxy}-(5u_{xx}v+10u_{xy}u-15u^2v)_x=0$ where $v_x=u_y$, thereby yielding their one-periodic and two-periodic wave solutions describing one dimensional propagation of waves

Finite-dimensional integrable systems associated with Davey-Stewartson I equation

For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained and their functional independence is proved. Therefore, the Hamiltonian systems are completely integrable in Liouville sense. A periodic solution of the Davey-Stewartson I equation is obtained by solving these classical Hamiltonian systems as an example.Comment: 18 pages, LaTe

Binary nonlinearization of the super AKNS system

We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finite-dimensional integrable Hamiltonian system in supersymmetry manifold $\mathbb{R}^{4N|2N}$. The super Hamiltonian forms and integrals of motion are given explicitly.Comment: 13pages, Latex, to appear in Modern Phys. Lett.

Consecutive Rosochatius Deformations of the Garnier System and the Hénon-Heiles System

An algorithm of constructing infinitely many symplectic realizations of generalized sl(2) Gaudin magnet is proposed. Based on this algorithm, the consecutive Rosochatius deformations of integrable Hamiltonian systems are presented. As examples, the consecutive Rosochatius deformations of the Garnier system and the Hénon-Heiles system as well as their Lax representations, are obtained

Adjoint Symmetry Constraints Leading to Binary Nonlinearization

Adjoint symmetry constraints are presented to manipulate binary nonlinearization, and shown to be a slight weaker condition than symmetry constraints in the case of Hamiltonian systems. Applications to the multicomponent AKNS system of nonlinear Schrodinger equations and the multi-wave interaction equations, associated with 33 matrix spectral problems, are made for establishing their integrable decompositions