Painlevé Singular Manifold Equation and Integrability
We recall the importance of the truncation procedure in PDE Painlevé analysis. Using the recently introduced invariant analysis, we define the singular manifold equations set, in both integrable and nonintegrable cases, as the condition for a truncated expansion to exist. As an application, we derive the correct form of this set for Sawada-Kotera equation.
KeywordsInvariant Analysis Determine Equation Schwarzian Derivative Truncation Procedure Sivashinsky Equation
Unable to display preview. Download preview PDF.
- M. Musette, Painleve-Darboux transformations in nonlinear partial differential equations, these proceedings.Google Scholar
- K. Sawada and T. Kotera, A method for finding N-soliton solutions of the K.d.V. equation and K.d.V.-like equations, Prog. Theor. Phys. 51, 1355–1367 (1974). P. J. Caudrey, R. K. Dodd and J. D. Gibbon, A new hierarchy of Korteweg-de Vries equations, Proc. Roy. Soc. London A351, 407–422 (1976).Google Scholar
- M. Musette and R. Conte, Third order Lax pair of the Hirota-Satsuma equation by a new invariant Painleve analysis, submitted for publication (1990).Google Scholar