 1915 Thomas Dreyfus, Alberto Lastra, Stephane Malek
 On the multiplescale analysis for some linear partial qdifference and differential equations with holomorphic coefficients
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Feb 1, 19

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Abstract. The analytic and formal solutions of certain family of qdifferencedifferential equations under the action of a complex perturbation parameter is considered. In a previous study the authors have provided information in the case when the main equation under study is factorizable, as a product of two equations in the socalled normal form. Each of them gives rise to a single level of qGevrey asymptotic expansion. In the present work, the main problem under study does not suffer any factorization, and a different approach is followed. More precisely, we lean on the technique developed in a recent paper of the first author, where he makes distinction among the different qGevrey asymptotic levels by successive applications of two qBorelLaplace transforms of different orders both to the same initial problem and which can be described by means of a Newton polygon.
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