Abstract

Several years ago, Ablowitz, Ramani and Segur made the Painleve 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 Painleve type. Here an ODE is said to be of Painleve 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 Painleve type [1,2].

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