完全可积的非线性方程建立哈密顿理论的一般方法和对SG方程应用

完全可积的非线性方程的单式矩阵的泊松括号已知可以表为对x的积分，指出被积函数一定 可以表为约斯特解对的直积的线性组合的微分，并可由直积矩阵相应元的对比确定组合系数 .从而解决了建立非线性方程哈密顿理论的一般方法.由于实验室系中的SG方程，相应的表述 异常复杂，所以以它为例来说明方法的实质.同时由于现有的相关工作违反了泊松括号同时 性的要求，给出了必要的改正.关键词：非线性方程哈密顿理论孤子

General procedure to formulate Hamiltonian theory of the completely integrable n onlinear equations and its application to the sine-Gordon equation

For a completely integrable nonlinear equation, the Poisson bracket of monodramy matrix is known to be expressed in a form of integral with respect to x. The in tegrand is found to be an x-differential of a linear combination of direct produ ct of two pairs of Jost solutions definitely, and the coefficients can be determ ined by comparing the corresponding elements of direct product matrices on two s ides. Hence a general procedure for constructing Hamiltonian formalism is given for a completely integrable nonlinear equation. As an example, the Hamiltonian t heory of sine-Gordon equation is re-examined, which shows the essence of the lin ear combination method for its very complicated Poisson bracket. And the previou s works involve, as is known, some inappropriate violating simultaneity of varia bles in Poisson bracket, which is also revised now.