Liouvillian and Darboux First Integrals of the Self-Assembling Micelle System

Wirya Mohommed Ramadhan; Azad Ibrahen Amin

doi:10.24996/ijs.2023.64.7.28

Authors

Wirya Mohommed Ramadhan Department of Mathematics, College of Education Basic Education, Salahaddin University - Erbil,Iraq. 2Department of Mathematics, Basic Education College, Raparin University - Ranya, Iraq. Department of Mathematics, Faculty of Science, Soran University - Soran, Erbil, Iraq.
Azad Ibrahen Amin Department of Mathematics, College of Education Basic Education, Salahaddin University - Erbil,Iraq. Department of Mathematics, Basic Education College, Raparin University - Ranya, Iraq. Department of Mathematics, Faculty of Science, Soran University - Soran, Erbil, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.7.28%20%20%20

Keywords:

Self-assembling micelle system, Invariant algebraic curves, Darboux first integrals, Darboux polynomials, Exponential factors, Weight homogeneous polynomials

Abstract

In this paper we prove that the planar self-assembling micelle system

has no Liouvillian, polynomial and Darboux first integrals. Moreover, we show that the system

has only one irreducible Darboux polynomial with the cofactor being if and only if via the weight homogeneous polynomials and only two irreducible exponential factors and with cofactors and respectively with be the unique Darbox invariant of system.