Integration of differential equations by $\mathcal{C}^{\infty}$-structures

Author:

A. J. Pan-Collantes, C. Muriel, A. Ruiz

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph), Dynamical Systems (math.DS)

journal:

Mathematics 2023, 11(18), 3897

date:

2023-08-27 16:00:00

Abstract

Several integrability problems of differential equations are addressed by using the concept of $\mathcal{C}^{\infty}$-structure, a recent generalization of the notion of solvable structure. Specifically, the integration procedure associated with $\mathcal{C}^{\infty}$-structures is used to integrate to a Lotka-Volterra model and several differential equations that lack sufficient Lie point symmetries and cannot be solved using conventional methods.

PDF: Integration of differential equations by $\mathcal{C}^{\infty}$-structures.pdf