This article presents a generalization, to nonintegrable equations, of the ARS-WTC method for the generation of singular solutions of PDE and ODE. The argument rests on the reduction of the equation to a generalized nonlinear Fuchsian equation and automatically ensures a representation of singularities by convergent expansions. Practical issues in the reduction process are emphasized. Finally, it is shown that a class of unstable characteristic singularities is related to the degeneration of noncharacteristic singularities.
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