ABSTRACT
This chapter describes some of the results of numerical investigations of the analytic structure in the complex t-plane. Many numerical integration techniques proceed with little knowledge of the precise positions and/or orders of the singularities encountered in the complex solution plane. It provides a Taylor series method that yields detailed information concerning the singularity nearest to the point of integration. The method is automatic in that one only needs to enter a statement of the o.d.es and such control parameters as initial conditions and path of integration. In certain studies of the integrability of partial differential equations and the inverse scattering transform method, some other areas the Painleve transcendents keep on popping up. A detailed analysis of the expansion about the singularity demonstrated that the solution is Painleve and depends on four arbitrary parameters.
