A geometric approach to higher-order Riccati chain: Darboux polynomials and constants of the motion

José F. Cariñena, Partha Guha, Manuel F. Rañada

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Abstract

The properties of higher-order Riccati equations are investigated. The second-order equation is a Lagrangian system and can be studied by using the symplectic formalism. The second-, third- and fourth-order cases are studied by proving the existence of Darboux functions. The corresponding cofactors are obtained and some related properties are discussed. The existence of generators of t-dependent constants of motion is also proved and then the expressions of the associated time-dependent first integrals are explicitly obtained. The connection of these time-dependent first integrals with the so-called master symmetries, characterizing some particular Hamiltonian systems, is also discussed. Finally the general n-th-order case is analyzed.

Original languageBritish English
Article number012009
JournalJournal of Physics: Conference Series
Volume175
Issue number1
DOIs
StatePublished - 2009
EventWorkshop on Higher Symmetries in Physics, WHSP 2008 - Madrid, Spain
Duration: 6 Nov 20088 Nov 2008

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