Liouvillian and Darboux First Integrals of the Self-Assembling Micelle System
Self-assembling micelle system
Invariant algebraic curves
Darboux first integrals
Darboux polynomials
Exponential factors
Weight homogeneous polynomials
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.
