Integration of first-order ODEs by Jacobi fields
Classical Analysis and ODEs
2024-04-30 v2 Differential Geometry
Abstract
A new class of vector fields enabling the integration of first-order ordinary differential equations (ODEs) is introduced. These vector fields are not, in general, Lie point symmetries. The results are based on a relation between 2-dimensional Riemannian manifolds and the integrability of first-order ODEs, which was established in a previous work of the authors. An integration procedure is provided, together with several examples to illustrate it. A connection between integrating factors of first-order ODEs and Schr\"odinger-type equations is highlighted.
Cite
@article{arxiv.2404.14352,
title = {Integration of first-order ODEs by Jacobi fields},
author = {A. J. Pan-Collantes and J. A. Alvarez-Garcia},
journal= {arXiv preprint arXiv:2404.14352},
year = {2024}
}