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

• 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
• ISSN: 2218-0230; 2412-3986

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.