关于Painlevé类方程的第一积分

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2023-08-27 DOI:10.1007/s40065-023-00441-0

Mogahid M. A. Ahmed, Bader Alqurashi, Abdul Hamid Kara

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引用次数: 0

摘要

对称性和第一积分的作用是众所周知的常微分方程（odes）的归约机制，并与之结合使用，导致odes的双重归约。在本文中，我们试图构造一大类著名的二阶Painlevé方程的第一积分。在某些情况下，变分和/或规范对称性在已知拉格朗日量之后具有额外的应用，在这种情况下，第一积分是通过Noether定理获得的。有时，采用“乘法器”方法来求第一积分更方便。在许多情况下，我们可以得出结论，该类是线性化的。

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On the first integrals of the Painlevé classes of equations

The role of symmetries and first integrals are well known mechanisms for the reduction of ordinary differential equations (odes) and, used in conjunction, lead to double reductions of the odes. In this article, we attempt to construct the first integrals of a large class of the well known second-order Painlevé equations. In some cases, variational and/or gauge symmetries have additional applications following a known Lagrangian in which case the first integral is obtained by Noether’s theorem. Sometimes, it is more convenient to adopt the ‘multiplier’ approach to find the first integrals. In a number of cases, we can conclude that the class is linearizable.

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.