一个复形式的C.Neumann系统与Jaulent-Miodek发展方程族的解

A Class of Complex C.Neumann System and Solvtions of the Hierarchy of the Janlent-Miodek Equation

利用谱问题的位势与特征函数之间的约束关系 ,将 Jaulent- Miodek发展方程族的L ax表示及其共轭形式进行非线性化 [1] ,并在实空间中引进一个合适的辛结构 ,Poisson括号和 Hamilton正则方程 ,导出了复形式的辛结构、Poisson括号和 Hamilton正则方程。进而证明被非线性化的 Lax表示化为一个完全可积的 C.Neumann系统。借助可换流的对合解 ,给出了Jaulent-

This paper is a continuation of solving the oliton equation by making use of the Hamiton methods.By means of the constraint between potentials and eigenfunctions of the Spectral Problem,the Lax Pairs of the hierarchy of the Janlent-Miodek equation are nonlinecrized;By means of Suitable Symplectic constraction,Poisson bracket and Hamiltonian canonical eqnation is introduced in the real space,their complex representations are obtained.Therefore,a finite climensional,completely integrable C.Neumann system is generated.Using the involntive soentions of the commutable flows,the solutions of the Jaulent-Miodek hierarchy are given.