@misc{10498/31835,
year = {2022},
month = {12},
url = {http://hdl.handle.net/10498/31835},
abstract = {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.},
publisher = {Elsevier},
keywords = {C∞-structure},
keywords = {C∞-symmetry of a distribution},
keywords = {Differential equations},
keywords = {Frobenius integrability},
keywords = {Solvable structure},
keywords = {Symmetry of a distribution},
title = {C∞-symmetries of distributions and integrability},
doi = {10.1016/j.jde.2022.11.051},
author = {Pan Collantes, Antonio Jesús and Ruiz Serván, Adrián and Muriel Patino, María Concepción and Romero, J. L.},
}