First integrals of nonlinear differential equations from nonlocal constants
Exactly Solvable and Integrable Systems
2023-05-02 v1 Mathematical Physics
math.MP
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 Painlev\'{e}-Gambier classification.
Cite
@article{arxiv.2305.00701,
title = {First integrals of nonlinear differential equations from nonlocal constants},
author = {Mattia Scomparin},
journal= {arXiv preprint arXiv:2305.00701},
year = {2023}
}
Comments
15 pages, 0 figures. arXiv admin note: text overlap with arXiv:2203.12219