英语翻译1．IntroductionIn soliton theory,constructing new integrable Hamiltonian systems is one of the mostimportant tasks．In recent years,a systemic approach,SO—called nonlinearization method of Lax pairs,was developed to generate new finit

英语翻译1．IntroductionIn soliton theory,constructing new integrable Hamiltonian systems is one of the mostimportant tasks．In recent years,a systemic approach,SO—called nonlinearization method of Lax pairs,was developed to generate new finit
英语翻译
1．Introduction
In soliton theory,constructing new integrable Hamiltonian systems is one of the most
important tasks．In recent years,a systemic approach,SO—called nonlinearization method of Lax pairs,was developed to generate new finite-dimensional integrable Hamiltonian systems from nonlinear evolution equations[1‘9|．With the help of the method,soliton equations may be decomposed into two compatible finite—dimensional integrable Hamiltonian systems．This procedure is called the integrable decomposition．The integrable decomposition can not only generate new finite—dimensional integrable systems,but also provide a way of solving soliton
equations．
In[1 o],Ma and Zhou studied a kind of multi—component AKNS equation by using the
binary non-linearization approach．In this paper,we would like to study another kind of multi—component AKNS equation by using the binary non—linearization approach．
This paper is organized as follows．In section 2,we construct the multi—component
AKNS hierarchy and its bi—Hamihonian structures．In section 3,FleW decompositions of the multi—component AKNS equation are obtained by using the binary non—linearization ap—proach．Furthermore,the integrability of the decomposition of the multi—component AKNS equation iS proved．

英语翻译1．IntroductionIn soliton theory,constructing new integrable Hamiltonian systems is one of the mostimportant tasks．In recent years,a systemic approach,SO—called nonlinearization method of Lax pairs,was developed to generate new finit
1. 介绍
在孤立子理论中,构造新的可积的汉密尔顿系统是最重要的任务之一.近几年,一个叫做拉克斯对非线性化法的系统方法得以发展,用来从非线性演变方程生成新的有限维的可积汉密尔顿系统.在此方法的帮助下,孤立子方程可以被分解为两个并立的有限维可积汉密尔顿系统,这个过程叫做可积分解.可积分解不仅能够生成新的有限维可积系统,还提供了一个解决孤立子方程的办法.
在参考文献10中,马和周两人运用二元非线性化法研究了一类多分量AKNS方程.在本文中,我们将要运用二元非线性化法研究另一类多分量AKNS方程.本文结构如下.在第二部分,我们构造该多分量AKNS层次及其二元汉密尔顿结构.在第三部分,运用二元非线性化法对多分量AKNS方程进行FLEW分解.然后,解决多分量AKNS方程的分解的可积问题.
AKNS,FLEW, Hamilton都是数学名词术语,有些有对应的中文翻译,有些没有.