RT journal article
T1 First Integrals of Differential Operators from SL(2, R) Symmetries
A1 Morando, Paola
A1 Muriel Patino, María Concepción
A1 Ruiz Serván, Adrián
A2 Matemáticas
K1 differential operator
K1 first integral
K1 solvable structure
K1 integrable distribution
AB The construction of first integrals for SL(2,R)-invariant nth-order ordinary differential equations is a non-trivial problem due to the nonsolvability of the underlying symmetry algebra sl(2,R). Firstly, we provide for n=2 an explicit expression for two non-constant first integrals through algebraic operations involving the symmetry generators of sl(2,R), and without any kind of integration. Moreover, although there are cases when the two first integrals are functionally independent, it is proved that a second functionally independent first integral arises by a single quadrature. This result is extended for n>2, provided that a solvable structure for an integrable distribution generated by the differential operator associated to the equation and one of the prolonged symmetry generators of sl(2,R) is known. Several examples illustrate the procedures.
PB MDPI
SN 2227-7390
YR 2020
FD 2020-12
LK http://hdl.handle.net/10498/24359
UL http://hdl.handle.net/10498/24359
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026