On the complete and partial integrability of non-Hamiltonian systems

T. C. Bountis, A. Ramani, B. Grammaticos, B. Dorizzi

Research output: Contribution to journalArticlepeer-review

69 Citations (Scopus)

Abstract

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In(t-t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

Original languageEnglish
Pages (from-to)268-288
Number of pages21
JournalPhysica A: Statistical Mechanics and its Applications
Volume128
Issue number1-2
DOIs
Publication statusPublished - Nov 1984

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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