%0 Journal Article 
%A Lastra Sedano, Alberto
%A Malek, Stephane
%T Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
%D 2018
%@ 1072-6691
%U http://hdl.handle.net/10017/41473
%X We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter ϵ. 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 ϵ 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 ϵ as Gevrey asymptotic expansion which might be different one to each other, in general.
%K Asymptotic expansion
%K Borel-Laplace transform
%K Fourier transform
%K Cauchy problem
%K Formal power series
%K Nonlinear integro-differential equation
%K Nonlinear partial differential equation
%K Singular perturbation
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala