First Integrals for Systems via Complex Partial Lagrangians

机译：通过复杂的局部拉格朗日方程式的系统的第一积分

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The partial Noether operators and partial Euler-Lagrange equations arerndeveloped for a system of k~(th)-order ordinary differential equations (ODEs) in the complexrndomain with the help of complex partial Lagrangians. A complex partial Noether theoremrnis deduced and the formula which provides the complex first integral is equivalent to therncomplex Noether integral. These complex partial Noether operators, in general, are notrncomplex symmetries of systems of complex ODEs and they are not closed. The theoremsrnare provided which give the condition of closure and when they become complex symmetryrngenerators is also stated. The results obtained in the complex domain are decomposed intornthe real domain for system of m second-order complex ODEs with m dependent variables.

机译：借助复偏拉格朗日算子，针对复数域中的k〜（阶）阶常微分方程（ODE）系统，开发了偏诺特算子和偏欧拉-拉格朗日方程。推导了一个复杂的部分Noether定理，并且提供复杂的第一个积分的公式等效于该复杂的Noether积分。这些复杂的部分Noether运算符通常是复杂ODE系统的非复杂对称性，并且它们不是封闭的。给出了给出闭合条件的定理，并指出了当它们变成复杂对称发生器时的情况。对于具有m个因变量的m个二阶复杂ODE系统，将其在复杂域中获得的结果分解为实域。

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来源
《Recent advances in business administration》|2010年|p.20-25|共6页
会议地点 Cambridge(GB);Cambridge(GB)
作者
I. NAEEM; R. NAZ; F. M. MAHOMED;
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作者单位

Department of Mathematics School of Science and Engineering Lahore university of management sciences Lahore Cantt 54792 Pakistan;

Centre for Mathematics and Statistical Sciences Lahore School of Economics Lahore 53200 Pakistan;

Centre for Differential Equations, Continuum Mechanics and Applications University of the Witwatersrand, Johannesburg Wits 2050 South Africa;

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原文格式 PDF
正文语种 eng
中图分类管理学;计算技术、计算机技术;
关键词
Euler operator; Total derivative; Gauge term; Partial Noether operators; CR equations; First integrals; Partial Lagrangian;

机译：欧拉算子；总导数；量规项；部分Noether运算符； CR方程；第一积分；部分拉格朗日;

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专利

1. First integrals for a general linear system of two second-order ODEs via a partial Lagrangian [J] . Naeem I, Mahomed FM Journal of physics, A. Mathematical and theoretical . 2008,第35期

机译：通过局部拉格朗日方程的两个二阶ODE的一般线性系统的第一积分
2. First Integrals of Two-Dimensional Dynamical Systems via Complex Lagrangian Approach [J] . Muhammad Umar Farooq, Chaudry Masood Khalique, Fazal M. Mahomed Symmetry . 2019,第10期

机译：二维动力学系统通过复杂拉格朗日方法的第一积分
3. Partial Noether operators and first integrals via partial Lagrangians [J] . Kara AH, Mahomed FM, Naeem I, Mathematical Methods in the Applied Sciences . 2007,第16期

机译：部分Noether算子和通过部分Lagrangian的第一积分
4. First Integrals for Systems via Complex Partial Lagrangians [C] . I. NAEEM, R. NAZ, F. M. MAHOMED WSEAS International Conference on Business Administration . 2010

机译：通过复杂的部分拉格朗吉亚人来说是系统的第一积分
5. Integral-equation methods for inhomogeneous elliptic partial differential equations in complex geometry. [D] . Askham, Travis. 2016

机译：复杂几何中非均匀椭圆偏微分方程的积分方程方法。
6. ON THE EXISTENCE OF INTEGRALS OF THE SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS Aαβii = 0 IN n VARIABLES [O] . Tracy Yerkes Thomas 1929

机译：n个变量中偏微分方程Aαβii= 0的系统积分的存在性
7. Bohmian trajectories and the Path Integral Paradigm. Complexified Lagrangian Mechanics [O] . Sbitnev, Valeriy I. 2008

机译：Bohmian轨迹和路径积分范式。 Complexified 拉格朗日力学

First Integrals for Systems via Complex Partial Lagrangians

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