Lax对变换与约束流的Lax表示

Lax对变换与约束流的Lax表示

张玉峰^1,2，张鸿庆¹

1. 大连理工大学应用数学系，大连 116024; 2. 山东科技大学信息学院，泰安 271019

收稿日期:2001-04-10 修回日期:1900-01-01 出版日期:2002-04-26 发布日期:2002-04-26
通讯作者: 张玉峰

Transformation of Lax Pair andLax Representation of Constrained Flows

ZHANG Yu-feng^1,2, ZHANG Hong-qing¹

1. Department of Applied Mathematics, Dalian University of Science and Technology, Dalian 116024, China;2. Information School, Shandong University of Science and Technology, Tai'an 271 019, China

Received:2001-04-10 Revised:1900-01-01 Online:2002-04-26 Published:2002-04-26
Contact: ZHANG Yu-feng

摘要/Abstract

摘要： 首先做一个恰当的Lax对变换，使变换前后的Lax对保持孤子方程族不变. 利用文献提供的方法，求出TD方程族约束流的Lax表示及在某约束条件下对称约束流的Hamilton结构.

关键词: Lax对变换, Lax表示, Hamilton结构, TD方程族

Abstract: A suitable transformation of Lax pair is made so as to make Lax pair before and after the transformation keep solution equations invariant. Then by means of the method proposed in refenrens ［1~4］ the Lax representation of constrained flows of TD hierarchy and the Hamiltonian structure of the symmetry constrained flows under some constrained condition are obtained.

Key words: transformation of Lax pair, Lax representation, Hamilto nian structure, TD hierarchy

中图分类号:

O175.29

张玉峰，张鸿庆. Lax对变换与约束流的Lax表示[J]. J4, 2002, 40(02): 114-118.

ZHANG Yu-feng, ZHANG Hong-qing. Transformation of Lax Pair andLax Representation of Constrained Flows[J]. J4, 2002, 40(02): 114-118.

[1]	牛艳秋, 杨双羚, 许明星. 一类三波作用模型的不变代数曲面、 Hamilton结构及无穷远动力学行为[J]. 吉林大学学报(理学版), 2019, 57(06): 1333-1338.
[2]	许明星, 周冉. 三维Lotka-Volterra系统的双Hamilton结构[J]. 吉林大学学报(理学版), 2019, 57(04): 773-778.
[3]	龚新波, 张玉峰. Loop代数A~₂的一个子代数与一族新的可积双Hamilton结构[J]. J4, 2003, 41(03): 269-271.