PAINLEVE PROPERTY AND HIROTA'S METHOD.

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

Research output: Contribution to journalArticle

72 Citations (Scopus)

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
StatePublished - Feb 1985
Externally publishedYes

Fingerprint

Painlevé
Solitons
Eigenvalues and eigenfunctions
Hirota Method
Painlevé Analysis
Partial differential equations
Scattering
Inverse Scattering Transform
Bäcklund Transformation
Soliton Solution
Eigenfunctions
Partial differential equation

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.

PAINLEVE PROPERTY AND HIROTA'S METHOD. / Gibbon, J. D.; Radmore, P.; Tabor, Michael; Wood, D.

In: Studies in Applied Mathematics, Vol. 72, No. 1, 02.1985, p. 39-63.

Research output: Contribution to journalArticle

Gibbon, JD, Radmore, P, Tabor, M & Wood, D 1985, 'PAINLEVE PROPERTY AND HIROTA'S METHOD.', Studies in Applied Mathematics, vol. 72, no. 1, pp. 39-63.
Gibbon JD, Radmore P, Tabor M, Wood D. PAINLEVE PROPERTY AND HIROTA'S METHOD. Studies in Applied Mathematics. 1985 Feb;72(1):39-63.
Gibbon, J. D. ; Radmore, P. ; Tabor, Michael ; Wood, D. / PAINLEVE PROPERTY AND HIROTA'S METHOD. In: Studies in Applied Mathematics. 1985 ; Vol. 72, No. 1. pp. 39-63.
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