On Singular Solutions to PDEs with Turning Point Involving a Quadratic Nonlinearity

We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter . The problem involves an irregular singularity in time, as in a recent work of the author and A. Lastra, but possesses also, as a new feature, a turning point at the origin in . We construct a family of sectorial meromorphic solutions obtained as a small perturbation in of a slow curve of the equation in some time scale. We show that the nonsingular parts of these solutions share common formal power series (that generally diverge) in as Gevrey asymptotic expansion of some order depending on data arising both from the turning point and from the irregular singular point of the main problem.

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