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We study a singularly perturbed PDE with cubic nonlinearity depending on acomplex perturbation parameter $\epsilon$. This is the continuation of aprecedent work by the first author. We construct two families of sectorialmeromorphic solutions obtained as a small perturbation in $\epsilon$ of twobranches of an algebraic slow curve of the equation in time scale. We show thatthe nonsingular part of the solutions of each family shares a common formalpower series in $\epsilon$ as Gevrey asymptotic expansion which might bedifferent one to each other, in general.

Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity