Singularities in the complex time plane and exactly solvable dynamical systems

A powerful tool in the study of nonlinear dynamical systems is the investigation of the singularity structure in the complex time plane. In most cases the singularity structure can only be found numerically. Here we give two models that can be solved exactly, i.e., we can give the singularities in the complex time plane. The two models play a central role in quantum mechanics. Then we compare them with the numerical study of the nonlinear differential equation.