On the multiple-scale analysis for some linear partial $q$-difference and differential equations with holomorphic coefficients
Abstract
The analytic and formal solutions of certain family of -difference-differential equations under the action of a complex perturbation parameter is considered. The previous study of the last two authors provides information in the case when 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 -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 a paper, where the first author makes distinction among the different -Gevrey asymptotic levels by successive applications of two -Borel-Laplace transforms of different orders both to the same initial problem and which can be described by means of a Newton polygon.
Cite
@article{arxiv.1704.00597,
title = {On the multiple-scale analysis for some linear partial $q$-difference and differential equations with holomorphic coefficients},
author = {Thomas Dreyfus and Alberto Lastra and Stéphane Malek},
journal= {arXiv preprint arXiv:1704.00597},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:1508.02621