Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
WTC expansions and non-integrable equations
This paper presents a generalization, to non-integrable 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 non-characteristic singularities.