Darboux polynomials and rational first integrals of the nonstretching Rolie–Poly model

In this paper, we classify irreducible Darboux polynomials and rational first integrals of the nonstretching Rolie–Poly model by a new method based on the classical characteristic curves method. The classical method has been successfully applied to many systems, but it is not suitable for the nonstretching Rolie–Poly model. We take it as an auxiliary tool to give a preliminary understanding of the structure of the Darboux polynomials, and obtain partial integrability results of the system.