On the multiple-scale analysis for some linear partial q-difference and differential equations with holomorphic coeffcients
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41534DOI: 10.1186/s13662-019-2263-5
ISSN: 1687-1839
Publisher
SpringerOpen
Date
2019-08-07Funders
European Commission
Ministerio de Economía y Competitividad
Bibliographic citation
Dreyfus, T., Lastra, A. & Malek, S. 2019, “On the multiple-scale analysis for some linear partial q-difference and differential equations with holomorphic coeficients”, Advances in Difference Equations, vol. 2019, no. 326
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Formal power series
Singular perturbation
q-difference-differential equation
Project
info:eu-repo/grantAgreement/EC/H2020/648132/EU/Automata in Number Theory/ANT
info:eu-repo/grantAgreement/MINECO//MTM2016-77642-C2-1-P/ES/Algebra y geometría en sistemas dinámicos y foliaciones singulares/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1186/s13662-019-2263-5Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
We consider analytic and formal solutions of certain family of q-difference-differential equations under the action of a complex perturbation parameter. The previous study (Lastra and Malek in Adv. Differ. Equ. 2015:344, 2015) provides information in the case where the main equation under study is factorizable as a product of two equations in the so-called normal form. Each of them gives rise to a single level of q-Gevrey 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 (Dreyfus in Int. Math. Res. Not. 15:6562-6587, 2015, where the first author makes distinction among the different q-Gevrey asymptotic levels by successive applications of two q-Borel-Laplace transforms of different orders, both to the same initial problem, which can be described by means of a Newton polygon.
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