127 citations · 780 across the 73 of their papers we have counts for
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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…
On the exact solutions of the Bianchi IX cosmological model in the proper time
J. Springael, R. Conte, M. Musette
It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three-parameter solution of Belin…
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…
A new method to test discrete Painlevé equations
R. Conte, M. Musette
Necessary discretization rules to preserve the Painlevé property are stated. A new method is added to the discrete Painlevé test, which perturbs the continuous limit and generates…
A geometrical method towards first integrals for dynamical systems
Simon Labrunie, Robert Conte
We develop a method, based on Darboux' and Liouville's works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without makin…
Non-Fuchsian extension to the Painlevé test
Micheline Musette, Robert Conte
We consider meromorphic particular solutions of nonlinear ordinary differential equations and perform a perturbation {\it à la} Poincaré making their linearized equation non-Fuchsi…