Chapman, S. J. and Mortimer, D. B. (2005) Exponential asymptotics and Stokes lines in a partial differential equation. Proceedings of the Royal Society of London A, 461 (2060). pp. 23852421. ISSN 13645021

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Abstract
A singularly perturbed linear partial differential equation motivated by the geometrical model for crystal growth is considered. A steepest descent analysis of the Fourier transform solution identifies asymptotic contributions from saddle points, end points and poles, and the Stokes lines across which these may be switched on and off. These results are then derived directly from the equation by optimally truncating the naïve perturbation expansion and smoothing the Stokes discontinuities. The analysis reveals two new types of Stokes switching: a higherorder Stokes line which is a Stokes line in the approximation of the late terms of the asymptotic series, and which switches on or off Stokes lines themselves; and a secondgeneration Stokes line, in which a subdominant exponential switched on at a primary Stokes line is itself responsible for switching on another smaller exponential. The ‘new’ Stokes lines discussed by Berk et al. (Berk et al. 1982 J. Math. Phys.23, 988–1002) are secondgeneration Stokes lines, while the ‘vanishing’ Stokes lines discussed by Aoki et al. (Aoki et al. 1998 In Microlocal analysis and complex Fourier analysis (ed. K. F. T. Kawai), pp. 165–176) are switched off by a higherorder Stokes line.
Item Type:  Article 

Subjects:  O  Z > Partial differential equations 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  295 
Deposited By:  Jon Chapman 
Deposited On:  03 Oct 2006 
Last Modified:  29 May 2015 18:19 
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