The University of Southampton
University of Southampton Institutional Repository

Hyperasymptotic solutions of inhomogeneous linear differential equations with a singularity of rank one

Hyperasymptotic solutions of inhomogeneous linear differential equations with a singularity of rank one
Hyperasymptotic solutions of inhomogeneous linear differential equations with a singularity of rank one
In this paper we discuss the special properties of hyperasymptotic solutions of inhomogeneous linear differential equations with a singularity of rank one. We show that the re-expansions are independent of the inhomogeneity.
We illustrate how this leads to a symmetry breaking in the Stokes constants within a pair of formal solutions of a differential equation. A consequence is that Stokes constants may exactly vanish in higher-order equations, leading to dramatic simplifications in the hyperasymptotic structures. Two examples are included.
asymptotic expansions, connection formulae, stokes multiplier, inhomogeneous differential equations, hyperasymptotics, irregular singularity
1364-5021
2599-2612
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Daalhuis, A.B.Olde
d2254863-03c9-4e12-aee7-2855b60dc933
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Daalhuis, A.B.Olde
d2254863-03c9-4e12-aee7-2855b60dc933

Howls, C.J. and Daalhuis, A.B.Olde (2003) Hyperasymptotic solutions of inhomogeneous linear differential equations with a singularity of rank one. Proceedings of the Royal Society A, 459 (2038), 2599-2612. (doi:10.1098/rspa.2003.1149).

Record type: Article

Abstract

In this paper we discuss the special properties of hyperasymptotic solutions of inhomogeneous linear differential equations with a singularity of rank one. We show that the re-expansions are independent of the inhomogeneity.
We illustrate how this leads to a symmetry breaking in the Stokes constants within a pair of formal solutions of a differential equation. A consequence is that Stokes constants may exactly vanish in higher-order equations, leading to dramatic simplifications in the hyperasymptotic structures. Two examples are included.

This record has no associated files available for download.

More information

Published date: 2003
Keywords: asymptotic expansions, connection formulae, stokes multiplier, inhomogeneous differential equations, hyperasymptotics, irregular singularity

Identifiers

Local EPrints ID: 29219
URI: http://eprints.soton.ac.uk/id/eprint/29219
ISSN: 1364-5021
PURE UUID: 32203be7-4e95-491e-99e3-a41f2d4f8b24
ORCID for C.J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

Catalogue record

Date deposited: 12 May 2006
Last modified: 28 Apr 2022 01:46

Export record

Altmetrics

Contributors

Author: C.J. Howls ORCID iD
Author: A.B.Olde Daalhuis

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×