A GENERALIZATION OF RECURSION OPERATORS OF DIFFERENTIAL EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (11): 1230-1236.

A GENERALIZATION OF RECURSION OPERATORS OF DIFFERENTIAL EQUATIONS

陈玉福^1,2, 张鸿庆¹

1. Institute of Mathematics Science, Dalian University of Technology, Dalian 116024, P. R. China;
2. Department of Mathematics, Jinzhou Normal College, Jinzhou, 121003, P. R. China

收稿日期:1998-05-22 修回日期:1999-05-22 出版日期:1999-11-18 发布日期:1999-11-18
基金资助:
the Foundation of Education Commission of Liaoning Province,China

A GENERALIZATION OF RECURSION OPERATORS OF DIFFERENTIAL EQUATIONS

Chen Yufu^1,2, Zhang Hongqing¹

1. Institute of Mathematics Science, Dalian University of Technology, Dalian 116024, P. R. China;
2. Department of Mathematics, Jinzhou Normal College, Jinzhou, 121003, P. R. China

Received:1998-05-22 Revised:1999-05-22 Online:1999-11-18 Published:1999-11-18
Supported by:
the Foundation of Education Commission of Liaoning Province,China

摘要/Abstract

摘要： Most important recursion operators of differential equations are integro-differential operators. One often runs into difficulties in trying to obtain a full hierarchy of symmetries. The lack of precision sometimes leads to bogus symmetries. In this paper, a generalization of recursion operators is given, which eliminates the problem. Several examples are also given to demonstrate the generalization and the significance of the generalization is shown simultaneously.

关键词: symmetries, recursion operators, prolongation of equations

Abstract: Most important recursion operators of differential equations are integro-differential operators. One often runs into difficulties in trying to obtain a full hierarchy of symmetries. The lack of precision sometimes leads to bogus symmetries. In this paper, a generalization of recursion operators is given, which eliminates the problem. Several examples are also given to demonstrate the generalization and the significance of the generalization is shown simultaneously.

Key words: symmetries, recursion operators, prolongation of equations

中图分类号:

O29
O175.3

陈玉福;张鸿庆. A GENERALIZATION OF RECURSION OPERATORS OF DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(11): 1230-1236.

Chen Yufu;Zhang Hongqing. A GENERALIZATION OF RECURSION OPERATORS OF DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(11): 1230-1236.

参考文献

[1] Olver P J.Evolution equations possessing infinitely many symmetries[J].J Math Phys,1997,18(6):1212～1215.
[2] Ablowits M J,Kaup D J,Newell A C,etal .The inverse Scattering transform——Fourier analysis for nonlinear problems[J].Stud Appl Math,1974,53(4):249～315.
[3] Miura R M,Gardner C S,Kruskal M D.Korteweg-de Vriesequationand generalizationsⅠ,Ⅱ[J].JMath Phys,1968,9(8):1202～1209.
[4] Magri F.Asimple model of the integrable Hamiltonian equations[J].JMath Phys,1978,19(5):1156～1162.
[5] Olver P J.Applications of Lie Groups to Differential Equations[M].New York;Springer-Verlag,1986.
[6] Krasil’ shchik I S,Vinogradov AM.Nonlocal treads in the geometry of differential equations,symmetries,conservation laws and Backlund transformations[J].Acta Appl Math,1989,15(2):161～209.
[7] Ayse Karasu,Jordan KdV systems and painleve property[J].Int J Theo Phys,1997,36(3):705～713.
[8] Khor’kova N G.Conservation laws and nonlocalsym metries[J].Math Notes,1989,44(4);562～568.
[9] Wahlquist H D,Estabrook F B.Prolongation structures of nonlinear evolution equations[J].J Math Phys,1975,16(1):1～7.
[10] Dodd R K.The general prolongation formulaefor nonlocalsym metries[J].Phys Lett,1994,A195;125～127.
[11] Bluman G W,Kumei S.Symmetries and Differential Equations[M].New York:Springer-Verlag,1989.
[12] Krasil’shchikIS,Kersten PH M.Deformations and recursion operators for evolution equation[A].Geometryin Partial Differential Equations[C].World Scientific Publishing Co.1994,114～155.
[13] Zhang Hongqing.Aunited theory on general solutions ofsystems of elasticity equations[J].Journal of Dalian University of Technology,1978,17(3):23～27.(in Chinese)
[14] Zhang Hongqing.The algebraization,mechanization,simplicization and geometrization of mechanics [A].In;Reports on MMM-Ⅶ[C] ,1997,20～25.(in Chinese)

A GENERALIZATION OF RECURSION OPERATORS OF DIFFERENTIAL EQUATIONS

A GENERALIZATION OF RECURSION OPERATORS OF DIFFERENTIAL EQUATIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	M.Tahir Mustafa Khalid Masood. Symmetry solutions of a nonlinear elastic wave equation with third-order anharmonic corrections[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(8): 1017-1026.
[2]	王文洽. THE ALTERNATING SEGMENT CRANK-NICOLSON METHOD FOR SOLVING CONVECTION-DIFFUSION EQUATION WITH VARIABLE COEFFICIENT[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(1): 32-42.
[3]	张鸿庆;朝鲁;唐立民. TAYLOR POLYNOMIAL STEPWISE REFINEMENTALGORITHM FOR LIE AND HIGH SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(3): 213-220.