Group classification of projective type second-order ordinary differential equations

Yu. Yu. Bagderina

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Group classification of projective type second-order ordinary differential equations

机译：射影型二阶常微分方程的组分类

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摘要

Group classification with respect to admitted point transformation groups is carried out for second-order ordinary differential equations with cubic nonlinearity of the first-order derivative. The result is obtained with use of the invariants of the equivalence transformation group of the family of equations under consideration. The corresponding Riemannian metric is found for the equations that are the projection of the system of geodesics to a two-dimensional surface.

机译：对于具有一阶导数的立方非线性的二阶常微分方程，对允许的点变换组进行组分类。通过使用所考虑方程组的等价变换组的不变量来获得结果。针对方程式找到了相应的黎曼度量，这些方程式是测地线系统到二维表面的投影。

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《Journal of applied and industrial mathematics》 |2016年第1期|共14页
作者
Yu. Yu. Bagderina;
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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
transformation group; symmetry; equivalence; invariant; group classification;

机译：变换群;对称性;对等性;不变性;群分类;

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专利

1. Group classification of projective type second-order ordinary differential equations [J] . Yu. Yu. Bagderina Journal of applied and industrial mathematics . 2016,第1期

机译：射影型二阶常微分方程的组分类
2. CARTAN PROJECTIVE CONNECTION SPACES AND GROUP-THEORETIC ANALYSIS OF SYSTEMS OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS [J] . A. V. Aminova, N. A.-M. Aminov Journal of Mathematical Sciences . 2010,第3期

机译：二阶常微分方程组的Cartan投影连接空间和群理论分析
3. Conditions for linearization of a projectable system of two second-order ordinary differential equations [J] . Sookmee S, Meleshko SV Journal of physics, A. Mathematical and theoretical . 2008,第40期

机译：两个二阶常微分方程的可投影系统的线性化条件
4. Group Classification of Systems of Two Linear Second-Order Stochastic Ordinary Differential Equations [C] . T.G. Mkhize, G.F. Oguis, K. Govinder, International Conferece on Modern Treatment of Symmetries, Differential Equations and Applications . 2019

机译：三个线性二阶随机常微分方程系统分类
5. ANALYSIS OF MULTISTEP METHODS FOR SPECIAL SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS. [D] . ASH, JAMES HOWARD. 1969

机译：特殊二阶常微分方程的多步法分析。
6. Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients [O] . Vyacheslav M. Boyko, Roman O. Popovych, Nataliya M. Shapoval -1

机译：常系数二阶线性常微分方程组的Lie对称性
7. On the Study of the General Group Classification of Systems of Linear Second-Order Ordinary Differential Equations [O] . Meleshko, S. V., Moyo, S. 2014

机译：关于线性系统一般群分类的研究二阶常微分方程
8. The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painleve Type [R] . McLeod, J. B., Olver, P. J. 1980

机译：反散射可解的偏微分方程与painleve型常微分方程的联系

Group classification of projective type second-order ordinary differential equations

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