常系数无穷维Hamilton系统的二阶循环算子结构

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 326-335.

常系数无穷维Hamilton系统的二阶循环算子结构

耿万鹏,任文秀*(),程意苏()

^{内蒙古工业大学理学院呼和浩特 010051}

收稿日期:2020-01-09 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 任文秀 E-mail:renwenxiu2003@hotmail.com;1070448132@qq.com
作者简介:程意苏, E-mail: 1070448132@qq.com

Second Order Recursion Operator Structure of Constant Coefficient Infinite Dimension Hamiltonian System

Wanpeng Geng,Wenxiu Ren*(),Yisu Cheng()

^{School of Sciences, Inner Mongolia University of Technology, Hohhot 010051}

Received:2020-01-09 Online:2021-04-26 Published:2021-04-29
Contact: Wenxiu Ren E-mail:renwenxiu2003@hotmail.com;1070448132@qq.com

摘要/Abstract

摘要：

该文借助于有限和形式的常系数Hamilton算子，将一般体系循环算子的获得方法应用到无穷维形式的Hamilton正则系统.在结果方面，获得了约束条件下一阶常系数Hamilton算子所允许的循环算子的一般结构及其系数的具体形式.又通过算例验证了结论的正确性与便捷性.

关键词: 常系数Hamilton算子, 无穷维线性Hamilton正则系统, 循环算子

Abstract:

By virtue of limited and formal constant coefficient Hamiltonian operator, it applies the method of general system recursion operator to Hamiltonian canonical system of infinite dimensional form. As to the result, the general structure of the recursion operator allowed by the next-order constant coefficient Hamiltonian operator under constraint condition and specific form of its coefficient are obtained. And then, it verifies the correctness and convenience of the conclusion by means of calculating example.

Key words: Constant coefficient Hamiltonian operator, Infinite dimensional linear Hamiltonian canonical system, Recursion operator

中图分类号:

O175

耿万鹏,任文秀,程意苏. 常系数无穷维Hamilton系统的二阶循环算子结构[J]. 数学物理学报, 2021, 41(2): 326-335.

Wanpeng Geng,Wenxiu Ren,Yisu Cheng. Second Order Recursion Operator Structure of Constant Coefficient Infinite Dimension Hamiltonian System[J]. Acta mathematica scientia,Series A, 2021, 41(2): 326-335.

参考文献 11

1	Olver P J . Evolution equation possessing infinitely many symmetries. Journal of Mathematical Physics, 1977, 18 (6): 1212- 1215 doi: 10.1063/1.523393
2	Bluman G W , Kumei S . Symmetries and Differential Equations. New York: Springer-Verlag, 1989
3	Gürses M . On construction of recursion operators from lax representation. Department of Mathematies, 1999, 40 (12): 6473- 6490
4	Stampp M , Karasu A . Recursion operators and Hamiltonian structures in sato's theory. Letters in Mathematical Physics, 1990, 20, 195- 210 doi: 10.1007/BF00398363
5	Wang J P . A list of 1+1 dimensional integrable equations and their properties. Journal of Nonlinear Mathematical Physics, 2002, 9 (1): 213- 233
6	Baldwin D E , Hereman W . A symbolic algorithm for computing recursion operators of nonlinear PEDs. International Journal of Computer Mathematics, 2010, 87 (5): 1094- 1119 doi: 10.1080/00207160903111592
7	Fokas A S , Fuchssteiner B . On the structure of symplectic operators and hereditary ymmetries. Lettere al Nuovo Cimento, 1980, 28 (8): 299- 303 doi: 10.1007/BF02798794
8	Wang Y , Li B , An H L . Dark Sharma-Tasso-Olver equations and their recursion operators. Chinese Physics Letters, 2018, 35 (1): 010201 doi: 10.1088/0256-307X/35/1/010201
9	李静. 无穷维Hamilton系统下循环算子及反问题的研究[D]. 呼和浩特: 内蒙古工业大学, 2017
	Li J. Study about recursion operators and inverse problem of infinite dimensional Hamiltonian system[D]. Huhehot: Inner Mongol University of Technology, 2017
10	霍晓霞, 任文秀. 二阶偏微分方程的Hamilton正则形式化的分类讨论. 内蒙古工业大学学报, 2019, 38 (1): 1- 7 doi: 10.3969/j.issn.1001-5167.2019.01.001
	Huo X X , Ren W X . A discussion on the classification of Hamilton canonical formalization of second order partial differential equations. Journal of Inner Mongol University of Technology, 2019, 38 (1): 1- 7 doi: 10.3969/j.issn.1001-5167.2019.01.001
11	许晶. 获得Hamilton系统下循环算子、守恒律的方法及应用[D]. 呼和浩特: 内蒙古工业大学, 2013
	Xu J. Obtaining methods and applications of recursion operators and conservation laws in the Hamiltonian system[D]. Huhehot: Inner Mongol University of Technology, 2013

[1]	王晓宏, 曹广福. Dirichlet空间上的循环复合算子[J]. 数学物理学报, 2003, 23(1): 91-95.
[2]	田立新, 刘曾荣. 无穷维线性空间中的非游荡算子[J]. 数学物理学报, 1995, 15(4): 455-460.