## On singular solutions to PDEs with turning point involving a quadratic nonlinearity.(English)Zbl 1470.35140

Summary: We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter $$\varepsilon$$. 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 $$\mathbb{C}$$. We construct a family of sectorial meromorphic solutions obtained as a small perturbation in $$\varepsilon$$ 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 $$\varepsilon$$ 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.

### MSC:

 35G20 Nonlinear higher-order PDEs 35B25 Singular perturbations in context of PDEs 35C20 Asymptotic expansions of solutions to PDEs
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### References:

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