Integrability of Differential Equations with Fluid Mechanics Application: from Painleve Property to the Method of Simplest Equation

@inproceedings{Dimitrova2013IntegrabilityOD,
  title={Integrability of Differential Equations with Fluid Mechanics Application: from Painleve Property to the Method of Simplest Equation},
  author={Zlatinka I. Dimitrova and Kaloyan N. Vitanov},
  year={2013}
}
We present a brief overview of integrability of nonlinear ordinary and partial differential equations with a focus on the Painleve property: an ODE of second order possesses the Painleve property if the only movable singularities connected to this equation are single poles. The importance of this property can be seen from the Ablowitz-Ramani- Segur conhecture that states that a nonlinear PDE is solvable by inverse scattering transformation only if each nonlinear ODE obtained by ex- act… CONTINUE READING
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