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On a q —Analog of a Singularly Perturbed Problem of Irregular Type with Two Complex Time Variables

Author

Listed:
  • Alberto Lastra

    (Departamento de Física y Matemáticas, University of Alcalá, Ap. de Correos 20, E-28871 Alcalá de Henares (Madrid), Spain
    These authors contributed equally to this work.)

  • Stéphane Malek

    (Laboratoire Paul Painlevé, University of Lille 1, 59655 Villeneuve d’Ascq CEDEX, France
    These authors contributed equally to this work.)

Abstract

The analytic solutions of a family of singularly perturbed q -difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic solutions, the so-called inner and outer solutions, are considered. Each of them holds a particular asymptotic relation with the formal ones in terms of asymptotic expansions in the perturbation parameter. The growth rate in the asymptotics leans on the − 1 -branch of Lambert W function, which turns out to be crucial.

Suggested Citation

  • Alberto Lastra & Stéphane Malek, 2019. "On a q —Analog of a Singularly Perturbed Problem of Irregular Type with Two Complex Time Variables," Mathematics, MDPI, vol. 7(10), pages 1-25, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:924-:d:273308
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