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

  • Sarbast Hussein Mikaeel Department of Mathematics, Faculty of Science, Soran University, Kurdistan Region, Iraq.
  • Azad I. Amen 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.
Keywords: Draboux First Integral; Invariant Algebraic Surfaces; Exponential Factor; Rational First integral.

Abstract

             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.

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References

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Published
2021-04-18
How to Cite
Mikaeel, S. and I. Amen, A. (2021) “Darboux and rational first integrals for a family of cubic three dimensional system”, Zanco Journal of Pure and Applied Sciences, 33(2), pp. 139-146. doi: 10.21271/ZJPAS.33.2.13.
Section
Mathematics ,Physics and Engineering Researches