20 citations · 50 across the 6 of their papers we have counts for
7 papers
Integration of differential equations by -structures
A. J. Pan-Collantes, C. Muriel, A. Ruiz
Several integrability problems of differential equations are addressed by using the concept of -structure, a recent generalization of the notion of solvable s…
-structures in the integration of involutive distributions
A. J. Pan-Collantes, C. Muriel, A. Ruiz +1
For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution of vector fields, the problem of its integration is considered. Among the many…
-symmetries of distributions and integrability
A. J. Pan-Collantes, A. Ruiz, C. Muriel +1
An extension of the notion of solvable structure for involutive distributions of vector fields is introduced. The new structures are based on a generalization of the concept of sym…
Generalized symmetries, first integrals, and exact solutions of chains of differential equations
C. Muriel, M. C. Nucci
New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied. The…
Symmetries and integrability by quadratures
C. Muriel, J. L. Romero, A. Ruiz
It is investigated how two (standard or generalized) symmetries of a given second-order ordinary differential equation can be used to solve the equation by quadratures. The met…
Solvable Structures Associated to the Nonsolvable Symmetry Algebra
Adrián Ruiz, Concepción Muriel
Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra admit solvable structures. These solvable…