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.
KeywordsNonlinear Evolution Equation Nonlinear Schrodinger Equation Backlund Transformation Integrable Dynamical System Painleve Property
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