一个有限维Hamilton系统的Liouville可积性研究

数学季刊 ›› 2011, Vol. 26 ›› Issue (1): 11-15.

一个有限维Hamilton系统的Liouville可积性研究

Department of Mathematics and Information Science, Zhengzhou University of Light Industry

收稿日期:2007-06-04 出版日期:2011-03-30 发布日期:2023-05-08
作者简介:ZHU Yun(1973- ), famale, native of Tanghe, Henan, a lecturer of Zhengzhou University of Light Industry, M.S.D., engages in foundation mathematics; YIN Li(1969- ), female, native of Xiping, Henan, an associate professor of Zhengzhou University of Light Industry, Ph.D., engages in foundation mathematics.
基金资助:
Supported by the NNSF of China(10701066)；

The Integrable in Liouville Sense of a Finite-dimensional Hamilton System

Department of Mathematics and Information Science, Zhengzhou University of Light Industry

Received:2007-06-04 Online:2011-03-30 Published:2023-05-08
About author:ZHU Yun(1973- ), famale, native of Tanghe, Henan, a lecturer of Zhengzhou University of Light Industry, M.S.D., engages in foundation mathematics; YIN Li(1969- ), female, native of Xiping, Henan, an associate professor of Zhengzhou University of Light Industry, Ph.D., engages in foundation mathematics.
Supported by:
Supported by the NNSF of China(10701066)；

摘要/Abstract

摘要： Based on a 2 × 2 eigenvalue problem, a set of (1 + 1)-dimensional soliton equations are proposed. Moreover, we obtain a finite dimensional Hamilton system with the help of nonlinearization approach. Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system, hence, we can verify it is completely integrable in Liouville sense.

关键词: (1+1)-dimension equation, Hamilton system, the generating function

Abstract: Based on a 2 × 2 eigenvalue problem, a set of (1 + 1)-dimensional soliton equations are proposed. Moreover, we obtain a finite dimensional Hamilton system with the help of nonlinearization approach. Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system, hence, we can verify it is completely integrable in Liouville sense.

Key words: (1+1)-dimension equation, Hamilton system, the generating function

中图分类号:

O172.2

朱云, 尹丽. 一个有限维Hamilton系统的Liouville可积性研究[J]. 数学季刊, 2011, 26(1): 11-15.

ZHU Yun, YIN Li. The Integrable in Liouville Sense of a Finite-dimensional Hamilton System [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 11-15.