The Painlevé Property and Hirota's Method
作者:
J. D. Gibbon,
P. Radmore,
M. Tabor,
D. Wood,
期刊:
Studies in Applied Mathematics
(WILEY Available online 1985)
卷期:
Volume 72,
issue 1
页码: 39-63
ISSN:0022-2526
年代: 1985
DOI:10.1002/sapm198572139
数据来源: WILEY
摘要:
The connection between the Painlevé property for partial differential equations, proposed by Weiss, Tabor, and Carnevale, and Hirota's method for calculatingN‐soliton solutions is investigated for a variety of equations including the nonlinear Schrödinger and mKdV equations. Those equations which do not possess the Painlevé property are easily seen not to have self‐truncating Hirota expansions. The Bäcklund transformations derived from the Painlevé analysis and those determined by Hirota's method are shown to be directly related. This provides a simple route for demonstrating the connection between the singular manifolds used in the Painlevé analysis and the eigenfunctions of the AKNS inverse scattering
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