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

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González Gascón, Francisco and Ramos, F.B. and 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

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


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Abstract

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


Item Type:Article
Uncontrolled Keywords:Partial differential equations; polynomials; langragian function; gauge invariance
Subjects:Sciences > Mathematics > Differential equations
ID Code:20654
Deposited On:04 Apr 2013 14:03
Last Modified:12 Dec 2018 15:14

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