Integrable systems without the Painlevé property. (English) Zbl 0953.34077
Summary: The authors examine whether the Painlevé property is a necessary condition for the integrability of nonlinear ordinary differential equations. They show that for a large class of linearizable systems this is not the case. In the discrete domain, they investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlevé continuous linearizable systems. They find that while these discrete systems are themselves linearizable, they possess nonconfined singularities.
MSC:
34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
39A12 | Discrete version of topics in analysis |
34A34 | Nonlinear ordinary differential equations and systems |
37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |