2026-08-20T17:00:32Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/647952023-08-27T03:55:26Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
González Gascón, Francisco
author
Ramos, F.B.
author
Aguirre Dabán, Eduardo
2023-06-21T02:04:39Z
2023-06-21T02:04:39Z
1982
1089-7658
http://0-link.aip.org.cisne.sim.ucm.es/link/doi/10.1063/1.525306
https://hdl.handle.net/20.500.14352/64795
http://0-link.aip.org.cisne.sim.ucm.es/link/doi/10.1063/1.525306
http://aip.org/
It is shown that any first integral of type P2()—a polynomial of degree 2 in —of the differential equation =Vx can be obtained from a pointlike gauge symmetry of the action AL associated to L= 1/2 2+V(t,x). The same result holds for any first integral of kind Pn() when dynamical symmetries of AL polynomials in are allowed. The neccessary and sufficient conditions that V(t,x) must satisfy in order that =Vx possesses a first integral of type Pn() have been obtained. These conditions reduce (when n=2) to a condition obtained by Leach. The computational advantages and difficulties which appear in order to obtain first integrals for type Pn() are also briefly discussed
On the polynomial first integrals of certain second‐order differential equations
journal article