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
2599-2612
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Daalhuis, A.B.Olde
d2254863-03c9-4e12-aee7-2855b60dc933
2003
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), .
(doi:10.1098/rspa.2003.1149).
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.
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Published date: 2003
Keywords:
asymptotic expansions, connection formulae, stokes multiplier, inhomogeneous differential equations, hyperasymptotics, irregular singularity
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Local EPrints ID: 29219
URI: http://eprints.soton.ac.uk/id/eprint/29219
ISSN: 1364-5021
PURE UUID: 32203be7-4e95-491e-99e3-a41f2d4f8b24
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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 03:13
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Author:
A.B.Olde Daalhuis
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