Stokes Phenomenon and Matched Asymptotic Expansions

作者: A. B. Olde Daalhuis , S. J. Chapman , J. R. King , J. R. Ockendon , R. H. Tew

DOI: 10.1137/S0036139994261769

关键词:

摘要: This paper describes the use of matched asymptotic expansions to illuminate description functions exhibiting Stokes phenomenon. In particular approach highlights way in which local structure and possibility finding multipliers explicitly depend on behaviour coefficients relevant expansions.

参考文章(11)
M V Berry, C J Howls, Stokes surfaces of diffraction catastrophes with codimension three Nonlinearity. ,vol. 3, pp. 281- 291 ,(1990) , 10.1088/0951-7715/3/2/003
Richard E. Meyer, On Exponential Asymptotics for Nonseparable Wave Equations I: Complex Geometrical Optics and Connection SIAM Journal on Applied Mathematics. ,vol. 51, pp. 1585- 1601 ,(1991) , 10.1137/0151080
V.Yu. Novokshenov, Nonlinear Stokes phenomenon for the second Painleve´ equation Physica D: Nonlinear Phenomena. ,vol. 63, pp. 1- 7 ,(1993) , 10.1016/0167-2789(93)90142-N
Smoothing of Stokes Discontinuities Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 437, pp. 343- 354 ,(1992) , 10.1098/RSPA.1992.0065
Frank W. J. Olver, Asymptotics and Special Functions ,(1974)
R. E. Meyer, A Simple Explanation of the Stokes Phenomenon SIAM Review. ,vol. 31, pp. 435- 445 ,(1989) , 10.1137/1031090
F J Wright, The Stokes set of the cusp diffraction catastrophe Journal of Physics A. ,vol. 13, pp. 2913- 2928 ,(1980) , 10.1088/0305-4470/13/9/018
Exponentially Improved Asymptotic Solutions of Ordinary Differential Equations. II Irregular Singularities of Rank One Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 445, pp. 39- 56 ,(1994) , 10.1098/RSPA.1994.0047
Uniform Asymptotic Smoothing of Stokes's Discontinuities Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 422, pp. 7- 21 ,(1989) , 10.1098/RSPA.1989.0018