Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
Texas State University, Department of Mathematics
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.
Asymptotic expansion, Borel-Laplace transform, Fourier transform, Cauchy problem, Formal power series, Nonlinear integro-differential equation, Nonlinear partial differential equation, Singular perturbation
Lastra, 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.
Attribution 4.0 International