数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2002年
2期
135-147
,共13页
分离变量%双约束流%Jacobi反演问题%Lax表示
分離變量%雙約束流%Jacobi反縯問題%Lax錶示
분리변량%쌍약속류%Jacobi반연문제%Lax표시
separation of variables%binary constrained flow%Jacobi inversion problem%Lax representation
本文给出了Tu方程族的高阶双约束流,其自由度为2N+l.根据通常的办法,利用Lax矩阵仅能引入N+l对标准分离变量和N+l个分离变量方程.本文构造出另外N对分离变量及N个分离变量方程.此外,还建立了双约束流和Tu方程族的Jacobi反演问题.
本文給齣瞭Tu方程族的高階雙約束流,其自由度為2N+l.根據通常的辦法,利用Lax矩陣僅能引入N+l對標準分離變量和N+l箇分離變量方程.本文構造齣另外N對分離變量及N箇分離變量方程.此外,還建立瞭雙約束流和Tu方程族的Jacobi反縯問題.
본문급출료Tu방정족적고계쌍약속류,기자유도위2N+l.근거통상적판법,이용Lax구진부능인입N+l대표준분리변량화N+l개분리변량방정.본문구조출령외N대분리변량급N개분리변량방정.차외,환건립료쌍약속류화Tu방정족적Jacobi반연문제.
Higher-order binary constrained flows of the Tu hierarchy are constructed.They have 2N + l degrees of freedom.For their separation of variables only N + l pairs of canonical separated variables can be introduced via their Lax matrices by using the normal method.We construct additional N pairs of canonical separated variables and N additional separated equations for the binary constrained flows of the Tu hierarchy.Furthermore,the Jacobi inversion problems for the binary constrained flows and for the Tu hierarchy are established.
