6 papers
Various truncations in Painlevé analysis of PDEs
R. Conte
The ``truncation procedure'' initiated by Weiss et al. is best understood as a Darboux transformation. If it leads to the Lax pair of the PDE under study, the Bäcklund transformati…
Perturbative methods for the Painlevé test
R. Conte
There exist many situations where an ordinary differential equation admits a movable critical singularity which the test of Kowalevski and Gambier fails to detect. Some possible re…
Rules of discretization for Painlevé equations
R. Conte, M. Musette
The discrete Painlevé property is precisely defined, and basic discretization rules to preserve it are stated. The discrete Painlevé test is enriched with a new method which pertur…
Towards second order Lax pairs to discrete Painlevé equations of first degree
R. Conte, M. Musette
We investigate the question of finding discrete Lax pairs for the six discrete Painlevé equations (Pn). The choice we make is to discretize the pairs of Garnier, once converted to…
The Painlevé approach to nonlinear ordinary differential equations
R. Conte
The ``Painlevé analysis'' is quite often perceived as a collection of tricks reserved to experts. The aim of this course is to demonstrate the contrary and to unveil the simplicity…
The Bianchi Ix (MIXMASTER) Cosmological Model is Not Integrable
A. ~Latifi, M. ~Musette, R. ~Conte
The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions whic…