Results 11 to 20 of about 10,861 (121)

Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point

Mathematics, 2020
This study is devoted to the description of the asymptotic expansions of solutions of linear ordinary differential equations with holomorphic coefficients in the neighborhood of an infinitely distant singular point.
Maria Korovina
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Boundary layer expansions for initial value problems with two complex time variables

Advances in Difference Equations, 2020
We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic ...
A. Lastra, S. Malek
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Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms

Advances in Difference Equations, 2020
This work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the
G. Chen, A. Lastra, S. Malek
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On Inner Expansions for a Singularly Perturbed Cauchy Problem with Confluent Fuchsian Singularities

Mathematics, 2020
A nonlinear singularly perturbed Cauchy problem with confluent Fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time.
Stephane Malek
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On Boundary Layer Expansions for a Singularly Perturbed Problem with Confluent Fuchsian Singularities

Mathematics, 2020
We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter ...
Stephane Malek
doaj   +1 more source

On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity

Mathematical and Computational Applications, 2019
The re-quantization method—one of the resurgent analysis methods of current importance—is developed in this study. It is widely used in the analytical theory of linear differential equations.
Maria Korovina, Ilya Smirnov, Vladimir Smirnov   +2 more
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On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms

Advances in Difference Equations, 2018
This paper is a continuation of the work (Lastra and Malek in J. Differ. Equ. 259(10):5220–5270, 2015) where singularly perturbed nonlinear PDEs have been studied from an asymptotic point of view.
Alberto Lastra, Stephane Malek
doaj   +1 more source

Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics [PDF]

, 1999
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help.
Balian R, Balian R, Bateman H, Bentosela F, Berry M V, Berry M V, Berry M V, Berry M V, Carlitz R N, Carlitz R N, Combes J-M, Delabaere E, Ecalle J, Ecalle J Cinq application des fonctions resurgentes, Eden R J, Fedoryuk M V, Fröman N, Giller S, Giller S, Giller S, Giller S, Hagedorn G A, Horzela A, Landau L D, Nicole D A, Simon B, Stefan Giller, Sternin B, Voros A, Zinn-Justin J   +29 more
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On the multiple-scale analysis for some linear partial q-difference and differential equations with holomorphic coefficients

Advances in Difference Equations, 2019
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
Thomas Dreyfus, Alberto Lastra, Stéphane Malek   +2 more
doaj   +1 more source

The resurgent character of the Fatou coordinates of a simple parabolic germ [PDF]

, 2014
Given a holomorphic germ at the origin of C with a simple parabolic fixed point, the local dynamics is classically described by means of pairs of attracting and repelling Fatou coordinates and the corresponding pairs of horn maps, of crucial importance ...
Dudko, Artem, Sauzin, David
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