4 papers
Painlevé analysis for nonlinear partial differential equations
M. Musette
The Painlevé analysis introduced by Weiss, Tabor and Carnevale (WTC) in 1983 for nonlinear partial differential equations (PDE's) is an extension of the method initiated by Painlev…
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 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…