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On the polynomial first integrals of certain second‐order differential equations

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González Gascón, Francisco y Ramos, F.B. y Aguirre Dabán, Eduardo (1982) On the polynomial first integrals of certain second‐order differential equations. Journal of Mathematical Physics, 23 (12). pp. 2281-2285. ISSN 1089-7658

URL Oficial: http://0-link.aip.org.cisne.sim.ucm.es/link/doi/10.1063/1.525306


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Resumen

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


Tipo de documento:Artículo
Palabras clave:Partial differential equations; polynomials; langragian function; gauge invariance
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:20654
Depositado:04 Abr 2013 14:03
Última Modificación:12 Dic 2018 15:14

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