Lax pairs, bäcklund transformations and special solutions for ordinary differential equations

J. D. Gibbon, A. C. Newell, M. Tabor, Y. B. Zeng

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

The authors investigate a modification of the Weiss-Tabor-Carnevale procedure that enables one to obtain Lax pairs and Backlund transformations for systems of ordinary differential equations. This method can yield both auto-Backlund transformations and, where necessary, Backlund transformations between different equations. In the latter case they investigate the circumstances under which the general Backlund transformations reduce to auto-Backlunds. In addition, special solution families for the second and fourth Painleve transcendents are obtained.

Original languageEnglish (US)
Pages (from-to)481-490
Number of pages10
JournalNonlinearity
Volume1
Issue number3
DOIs
StatePublished - Aug 1988

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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