RT journal article
T1 C∞-symmetries of distributions and integrability
A1 Pan Collantes, Antonio Jesús
A1 Ruiz Serván, Adrián
A1 Muriel Patino, María Concepción
A1 Romero, J. L.
A2 Matemáticas
K1 C∞-structure
K1 C∞-symmetry of a distribution
K1 Differential equations
K1 Frobenius integrability
K1 Solvable structure
K1 Symmetry of a distribution
AB An extension of the notion of solvable structure for involutive distributions of vector fields is introduced. It is based on a generalization of the concept of symmetry of a distribution of vector fields, inspired in the extension of Lie point symmetries to C∞-symmetries for ODEs developed in the recent years. The new structures, named C∞-structures, play a fundamental role in the integrability of the distribution: the knowledge of a C∞-structure for a corank k involutive distribution allows to find its integral manifolds by solving k successive completely integrable Pfaffian equations. These results have important consequences for the integrability of differential equations. In particular, we derive a new procedure to integrate an mth-order ordinary differential equation by splitting the problem into m completely integrable Pfaffian equations. This step-by-step integration procedure is applied to fully integrate several equations that cannot be solved by standard procedures.
PB Elsevier
SN 0022-0396
YR 2022
FD 2022-12-07
LK http://hdl.handle.net/10498/31835
UL http://hdl.handle.net/10498/31835
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026