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

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.

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