Similarity reductions from extended Painlevé expansions for nonintegrable evolution equations

F. Cariello, M. Tabor

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


The use of singular manifold expansions to find exact solutions to nonintegrable evolution equations is extended to include arbitrary (resonance) coefficients in such a way as to make the resulting infinite series exactly resummable. The technique involves the use of a rescaling ansatz analogous to that used to analyze the psi-series of nonintegrable ordinary differential equations. The result is a similarity reduction of the equation in which the constrained singular manifold plays the role of a similarity variable. The method is capable of yielding new solutions corresponding to either classical or nonclassical (conditional) Lie symmetries.

Original languageEnglish (US)
Pages (from-to)59-70
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Issue number1
StatePublished - Oct 1991
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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