一类孤子方程族及其多个Hamilton结构

A Type of Soliton Hierarchy and Its Multi-Hamiltonian Structures

本文建立了一个含11个位势的新的等谱问题,得到了一组新的Lax对,由此得到一类新的孤子方程族.该族是Liouville可积的,具有4-Hamilton结构,且循环算子的共轭算子是一个遗传对称算子.另外,为确切说明所得方程族是一个4-Hamilton结构,在附录中证明了所得的4个Hamilton算子的线性组合恒为Hamilton算子.

First a new isospectral problem with 11 potentials is established in the present paper. That a new Lax pair is presented whence, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses 4-Hamiltonian structures. It is proved that the conjugate operator of the recursive operator is of hereditary symmetry, after making some reductions, the well-known AKNS hierarchy and the other hierarchies of evolution equations are obtained. In addition, in order to illustrate that the soliton hierarchy obtained in the paper possesses 4-Hamiltonian structures exactly, we prove that the linear combination of 4-Hamiltonian operators admitted are also a Hamiltonian operator constantly.