PAINLEVE PROPERTY AND HIROTA'S METHOD.

J. D. Gibbon, P. Radmore, Michael Tabor, D. Wood

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73 Scopus citations

Abstract

The connection between the Painleve property for partial differential equations, proposed by J. Weiss et al. and R. Hirota's method for calculating N-soliton solutions is investigated for a variety of equations including the nonlinear Schroedinger and mKdV equations. Those equations which do not possess the Painleve property are easily seen not to have self-truncating Hirota expansions. The Backlund transformations derived from the Painleve 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 Painleve analysis and the eigenfunctions of the AKNS inverse scattering transform.

Original languageEnglish (US)
Pages (from-to)39-63
Number of pages25
JournalStudies in Applied Mathematics
Volume72
Issue number1
Publication statusPublished - Feb 1985
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Gibbon, J. D., Radmore, P., Tabor, M., & Wood, D. (1985). PAINLEVE PROPERTY AND HIROTA'S METHOD. Studies in Applied Mathematics, 72(1), 39-63.