First integrals of nonlinear differential equations from nonlocal constants

2023/05/01 by Scomparin, Mattia
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2305.00701

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.

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