[1]梁小花,张金顺.一个N维Hamilton系统的Painleve′分析与精确解[J].华侨大学学报(自然科学版),2007,28(3):327-329.[doi:10.3969/j.issn.1000-5013.2007.03.027]
　LIANG Xiao-hua,ZHANG Jin-shun.Painleve′ Test and Explicit Solution for a N Dimensional Hamiltonian System[J].Journal of Huaqiao University(Natural Science),2007,28(3):327-329.[doi:10.3969/j.issn.1000-5013.2007.03.027]
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一个N维Hamilton系统的Painleve′分析与精确解()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第28卷
期数:
2007年第3期
页码:
327-329
栏目:
出版日期:
2007-07-20

文章信息/Info

Title:
Painleve′ Test and Explicit Solution for a N Dimensional Hamiltonian System
文章编号:
1000-5013(2007)03-0327-03
作者:
梁小花; 张金顺
华侨大学数学科学学院; 华侨大学数学科学学院 福建泉州362021; 福建泉州362021
Author(s):
LIANG Xiao-hua;  ZHANG Jin-shun
College of Mathematics Science, Huaqiao University, Quanzhou 362021, China
关键词:
Painleve′分析;  Hamilton系统;  Bckland变换;  Schwardz导数
Keywords:
Painleve′ test;  Hamiltonian system;  Bckland transfomation;  Schwarz derivative
分类号:
O193
DOI:
10.3969/j.issn.1000-5013.2007.03.027
文献标志码:
A
摘要:
考虑一个Hamilton函数为H=1/2+1/22+1/2<Λp,p>的N维Hamilton系统,它与无穷维可积系统的经典例子——Kdv方程的Lax对密切相关的.利用Painleve′分析的方法,证明该N维Hamilton系统的是完全可积的,并得到其自Bckland变换.通过研究相关的Schwardz导数方程的性质,求出系统解的内积形式的精确表达式及Jacobi椭圆函数形式的解.
Abstract:
In this paper we consider a N dimensional Hamiltonian system with Hamiltonian function:H=1/2+1/22+1/2<Λp,p>.It has a relation with the Lax pairs of KdV equation.The integrability is proved and an auto-Bckland transfomation is obtained by means of the Painleve′ test.Explicit solutions in inner product form are also obtained for the N dimensional Hamiltonian system.

参考文献/References:

[1] CAO Ce-wen. Acta mathematics sinica [J]. New Series, 1991(7):216-223.
[2] ZHANG J S. Explicit solutions of a finite-dimensional integrable system [J]. Physics Letters A, 2005, (348):24-27.
[3] WEISS J, TABOR M, CARNEVALE G. The painleve property for partial differential equation [J]. Journal of Mathematical Physics, 1984, (24):329-331.
[4] CONTE R, MUSETTE M, GRUNDLAND A M. A reduction of the resonant three-wave interation to the generic six painleve equation [J]. Journal of Physics A:Mathematical and General, 2006, (39):12115-12127.
[5] STEEB W H, EULER N. Nonlinear evolution equations and Painleve′ test [M]. Sigapore:World Scientetifis, 1988.

备注/Memo

备注/Memo:
国务院侨办科研基金资助项目(06QZR12); 华侨大学科研基金资助项目(07BS106)
更新日期/Last Update: 2014-03-23