In this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equations (Burgers' equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.
|Original language||English (US)|
|Number of pages||5|
|Journal||Journal of Mathematical Physics|
|State||Published - Dec 1 1982|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics