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

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

In this paper, we investigate the first integrals of the following system exam.PNG exam1.PNG This kind of system is a particular case of the jerk cubic three dimensional polynomial differential systems. Generally, numerous several methods can be used to investigate t...

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Main Authors: Sarbast Hussein Mikaeel, Azad I. Amen
Format: Article
Language:English
Published: Salahaddin University-Erbil 2021-04-01
Series:Zanco Journal of Pure and Applied Sciences
Subjects:
draboux first integral; invariant algebraic surfaces; exponential factor; rational first integral.
Online Access:https://zancojournals.su.edu.krd/index.php/JPAS/article/view/3836
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spelling doaj-e516b37442cb49088dff84b6b9734f172021-04-26T07:23:49ZengSalahaddin University-ErbilZanco Journal of Pure and Applied Sciences2218-02302412-39862021-04-0133213914610.21271/ZJPAS.33.2.13Darboux and rational first integrals for a family of cubic three dimensional systemsSarbast Hussein Mikaeel0Azad I. Amen1Department of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq.1 Department of Mathematics, College of Basic Education, Salahaddin University, Kurdistan Region, Iraq. ^*Department of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq. ^⋆Department of Mathematics, College of Basic Education, University of Raparin, Kurdistan Region, Iraq. In this paper, we investigate the first integrals of the following system exam.PNG exam1.PNG This kind of system is a particular case of the jerk cubic three dimensional polynomial differential systems. Generally, numerous several methods can be used to investigate the first integral, but unfortunately most of them are not enable for finding first integrals. In this study Darboux method has been used to study the first integrals for the generalized the system for all parameters. Finally we seen that the system does not admit Darboux first integral and rational first integrals.https://zancojournals.su.edu.krd/index.php/JPAS/article/view/3836draboux first integral; invariant algebraic surfaces; exponential factor; rational first integral.
collection DOAJ
language English
format Article
sources DOAJ
author Sarbast Hussein Mikaeel
Azad I. Amen
spellingShingle Sarbast Hussein Mikaeel
Azad I. Amen
Darboux and rational first integrals for a family of cubic three dimensional systems
Zanco Journal of Pure and Applied Sciences
draboux first integral; invariant algebraic surfaces; exponential factor; rational first integral.
author_facet Sarbast Hussein Mikaeel
Azad I. Amen
author_sort Sarbast Hussein Mikaeel
title Darboux and rational first integrals for a family of cubic three dimensional systems
title_short Darboux and rational first integrals for a family of cubic three dimensional systems
title_full Darboux and rational first integrals for a family of cubic three dimensional systems
title_fullStr Darboux and rational first integrals for a family of cubic three dimensional systems
title_full_unstemmed Darboux and rational first integrals for a family of cubic three dimensional systems
title_sort darboux and rational first integrals for a family of cubic three dimensional systems
publisher Salahaddin University-Erbil
series Zanco Journal of Pure and Applied Sciences
issn 2218-0230
2412-3986
publishDate 2021-04-01
description In this paper, we investigate the first integrals of the following system exam.PNG exam1.PNG This kind of system is a particular case of the jerk cubic three dimensional polynomial differential systems. Generally, numerous several methods can be used to investigate the first integral, but unfortunately most of them are not enable for finding first integrals. In this study Darboux method has been used to study the first integrals for the generalized the system for all parameters. Finally we seen that the system does not admit Darboux first integral and rational first integrals.
topic draboux first integral; invariant algebraic surfaces; exponential factor; rational first integral.
url https://zancojournals.su.edu.krd/index.php/JPAS/article/view/3836
work_keys_str_mv AT sarbasthusseinmikaeel darbouxandrationalfirstintegralsforafamilyofcubicthreedimensionalsystems
AT azadiamen darbouxandrationalfirstintegralsforafamilyofcubicthreedimensionalsystems
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