Solitons pp 145-161 | Cite as

Painlevé Analysis and Integrability Aspects of Nonlinear Evolution Equations

  • M. Lakshmanan
  • K. M. Tamizhmani
Conference paper
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)


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.


Nonlinear Evolution Equation Nonlinear Schrodinger Equation Backlund Transformation Integrable Dynamical System Painleve Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • M. Lakshmanan
    • 1
  • K. M. Tamizhmani
    • 2
  1. 1.Department of PhysicsBharathidasan UniversityTiruchirapalliIndia
  2. 2.Department of MathematicsPondicherry UniversityPondicherryIndia

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