Splitting differential equations using Galois theory

Christine Eagles; Léo Jimenez

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arXiv · 2403.14900

Splitting differential equations using Galois theory

Christine Eagles·Léo Jimenez

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Abstract

This article is interested in pullbacks under the logarithmic derivative of algebraic ordinary differential equations. In particular, assuming the solution set of an equation is internal to the constants, we would like to determine when its pullback is itself internal to the constants. To do so, we develop, using model-theoretic Galois theory and differential algebra, a connection between internality of the pullback and the splitting of a short exact sequence of algebraic Galois groups. We then use algebraic group theory to obtain internality and non-internality results.

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BibTeX RIS

Christine Eagles, Léo Jimenez. 2024-03-22. Splitting differential equations using Galois theory. https://arxiv.org/abs/2403.14900

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