Alberto Lastra, Stephane Malek
Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
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ABSTRACT. We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter. This is the continuation of a precedent work by the first author focusing on a quadratic nonlinearity.
We construct two families of sectorial meromorphic solutions obtained as a small perturbation of two branches of an algebraic slow curve of the equation in some well chosen time scale. We show that the nonsingular part of the solutions of each family share a common formal power series in the perturbation parameter as Gevrey asymptotics which might be surprisingly different one to each other, in general.