Alberto Lastra, Stephane Malek
We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter . This is a continuation of the precedent work  by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in as Gevrey asymptotic expansion which might be different one to each other, in general.
Submitted July 6, 2017. Published February 13, 2018.
Math Subject Classifications: 35C10, 35C20.
Key Words: Asymptotic expansion; Borel-Laplace transform; Fourier transform; Cauchy problem; formal power series; nonlinear integro-differential equation; nonlinear partial differential equation; singular perturbation.
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| Alberto Lastra |
Dpto. de Física y Matemáticas
Universidad de Alcalá, Ap. Correos 20
E-28871 Alcalá de Henares, Madrid, Spain
| Stephane Malek |
University of Lille 1, Laboratoire Paul Painlevé
59655 Villeneuve d'Ascq cedex, France
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