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On the higher order Stokes phenomenon

On the higher order Stokes phenomenon
On the higher order Stokes phenomenon
During the course of a Stokes phenomenon, an asymptotic expansion can change its form as a further series, prefactored by an exponentially small term and a Stokes multiplier, appears in the representation. The initially exponentially small contribution may nevertheless grow to dominate the behaviour for other values of the asymptotic or associated parameters. In this paper we introduce the concept of a 'higher-order Stokes phenomenon', at which a Stokes multiplier itself can change value. We show that the higher-order Stokes phenomenon can be used to explain the apparent sudden birth of Stokes lines at regular points and how it is indispensable to the proper derivation of expansions that involve three or more possible asymptotic contributions. We provide an example of how the higher-order Stokes phenomenon can have important effects on the large-time behaviour of partial differential equations.
asymptotic expansions, hyperasymptotics, partial differential equations, steepest descent, Stokes phenomenon, turning points
1364-5021
2285-2303
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Langman, P.J.
b3d47d27-214b-478d-ba78-9c323f2f17ea
Daalhuis, A.B.O.
6b385a57-b024-4e2e-9f15-ceb2bfc5483a
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Langman, P.J.
b3d47d27-214b-478d-ba78-9c323f2f17ea
Daalhuis, A.B.O.
6b385a57-b024-4e2e-9f15-ceb2bfc5483a

Howls, C.J., Langman, P.J. and Daalhuis, A.B.O. (2004) On the higher order Stokes phenomenon. Proceedings of the Royal Society A, 460 (2048), 2285-2303. (doi:10.1098/rspa.2004.1299).

Record type: Article

Abstract

During the course of a Stokes phenomenon, an asymptotic expansion can change its form as a further series, prefactored by an exponentially small term and a Stokes multiplier, appears in the representation. The initially exponentially small contribution may nevertheless grow to dominate the behaviour for other values of the asymptotic or associated parameters. In this paper we introduce the concept of a 'higher-order Stokes phenomenon', at which a Stokes multiplier itself can change value. We show that the higher-order Stokes phenomenon can be used to explain the apparent sudden birth of Stokes lines at regular points and how it is indispensable to the proper derivation of expansions that involve three or more possible asymptotic contributions. We provide an example of how the higher-order Stokes phenomenon can have important effects on the large-time behaviour of partial differential equations.

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More information

Published date: 2004
Keywords: asymptotic expansions, hyperasymptotics, partial differential equations, steepest descent, Stokes phenomenon, turning points

Identifiers

Local EPrints ID: 29222
URI: http://eprints.soton.ac.uk/id/eprint/29222
ISSN: 1364-5021
PURE UUID: 04aa7537-11da-4383-bac2-ef79e6ee9fb7
ORCID for C.J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

Catalogue record

Date deposited: 11 May 2006
Last modified: 09 Jan 2022 03:03

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Contributors

Author: C.J. Howls ORCID iD
Author: P.J. Langman
Author: A.B.O. Daalhuis

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