36 citations · 149 across the 18 of their papers we have counts for
20 papers
Differential Galois Theory and Integration
Thomas Dreyfus, Jacques-Arthur Weil
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illus…
Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
Primitivo Acosta-Humánez, Moulay Barkatou, Raquel Sánchez-Cauce +1
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprising…
Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz
Moulay Barkatou, Thomas Cluzeau, Lucia Di Vizio +1
Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduc…
Computing the Lie algebra of the differential Galois group: the reducible case
Thomas Dreyfus, Jacques-Arthur Weil
In this paper, we explain how to compute the Lie algebra of the differential Galois group of a reducible linear differential system. We achieve this by showing how to transform a b…
Liouville integrability: an effective Morales-Ramis-Simó theorem
Ainhoa Aparicio-Monforte, Thomas Dreyfus, Jacques-Arthur Weil
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the inte…
Galoisian Methods for Testing Irreducibility of Order Two Nonlinear Differential Equations
Guy Casale, Jacques-Arthur Weil
The aim of this article is to provide a method to prove the irreducibility of non-linear ordinary differential equations by means of the differential Galois group of their variatio…