Lastra, AlbertoMalek, Stephane2022-01-072022-01-072018-02-13Lastra, A., & Malek, S. (2018). Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity. <i>Electronic Journal of Differential Equations, 2018</i>(46), pp. 1-89.1072-6691https://hdl.handle.net/10877/15102We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter ε. This is a continuation of the precedent work [22] 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.Text89 pages1 file (.pdf)enAttribution 4.0 InternationalAsymptotic expansionBorel-Laplace transformFourier transformCauchy problemFormal power seriesNonlinear integro-differential equationNonlinear partial differential equationSingular perturbationArticle