First integrals of nonlinear differential equations from nonlocal constants
Mattia Scomparin

Abstract. Abstract. A new method to find first integrals of nonlinear differential equations in Jacobi-type form is presented. The basic idea of our approach is to use one-parameter perturbed motions to find well-conceived nonlocal constants that are conserved along solutions. By means of such nonlocal framework we derive a set of theorems that we apply to look for the first integrals of some relevant cases, where moreover a solution is obtained. Applications also include some equations of the Painlevé-Gambier classification

Rend. Mat. Appl. (7) 44 (2023) 267-279; pdf