Painlevé Analysis and Integrability Aspects of Nonlinear Evolution Equations
A brief review of the singularity structure aspects of the solutions of nonlinear ordinary differential equations and their generalization to partial differential equations leading to the Painlevé (P) property is given. It is pointed out that the Painlevé analysis leads naturally to Lax pairs, Bäcklund transformations, linearizations and Hirota’s bilinearization of nonlinear evolution equations. Specifically we treat the Burgers’, Liouville, Korteweg-de Vries, coupled nonlinear Schrödinger and Kadomtsev -Petviashvili equations as examples.
Unable to display preview. Download preview PDF.
- P. J. Olvej., Applications ot Lie Groups to Differential Equations (Springer, New York, 1986).Google Scholar
- E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956).Google Scholar
- K. M. Tamizhmani, “Geometrical, Group Theoretical and Singularity Structure Analysis Aspects of Certain Nonlinear Partial Differential Equations,” Ph.D. Thesis, University of Madras (1986).Google Scholar
- A. Ramani, B. Dorizzi and B. Grammaticos, J. Math. Phys. 24 (1983) 2252.Google Scholar