Darboux and rational first integrals for a family of cubic three dimensional system

In this paper, we investigate the first integrals of the following system where and , . This kind of system is a special case of three-dimensional polynomial cubic differential systems. Generally, several methods can be used to investigate the first integrals, but unfortunately, most of them are...

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Bibliographic Details
Published in:	Zanco journal of pure and applied sciences Vol. 33; no. 2
Main Authors:	Sarbast H. Mikaeel, Azad I. Amen
Format:	Journal Article
Language:	English
Published:	Salahaddin University-Erbil 14-04-2021
Subjects:	Draboux First Integral; Invariant Algebraic Surfaces; Exponential Factor; Rational First integral
Online Access:	Get full text
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Summary:	In this paper, we investigate the first integrals of the following system where and , . This kind of system is a special case of three-dimensional polynomial cubic differential systems. Generally, several methods can be used to investigate the first integrals, but unfortunately, most of them are not enabled for finding first integrals. In this study, the Darboux method has been used to study the first integrals for the generalized system for all parameters. We characterize all its invariant algebraic surfaces and all its exponential factors of that system. We have shown that the above system does not admit a polynomial, rational, and Darboux first integrals for any values of the parameters.
ISSN:	2218-0230 2412-3986
DOI:	10.21271/ZJPAS.33.2.13