A New Approach to Completely Integrable Partial Differential Equations by Means of the Singularity Analysis

  • Hitoshi Harada
  • Shin’ichi Oishi
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)


Several years ago, Ablowitz, Ramani and Segur made the Painlevé conjecture in [1]: every nonlinear ordinary differential equation (ODE) obtained by an exact reduction of a completely integrable nonlinear partial differential equation (PDE) is of Painlevé type. Here an ODE is said to be of Painlevé type if its general solution has no movable singularities other than poles. Moreover they presented an explicit algorithm to test whether a given ODE satisfies certain necessary conditions for it to be of Painlevé type [1,2].


Nonlinear Partial Differential Equation Nonlinear Ordinary Differential Equation Soliton Equation Indicial Equation Movable Singularity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Hitoshi Harada
    • 1
  • Shin’ichi Oishi
    • 1
  1. 1.Department of Electronics and Communication Engineering, School of Science and EngineeringWaseda UniversityTokyo 160Japan

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