Non-generic connections corresponding to front solutions

J. Powell, Michael Tabor

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

A classification of special 'nonlinear' front solutions for certain one-time and one-space reaction-diffusion equations is presented, using the method of Weiss, Tabor and Carnevale (WTC). These results are related to known stability criteria, in particular the steepness criterion of van Saarloos (1989). The WTC method is shown to be equivalent to a special first-order reduction, and both of these methods are shown to work for reaction-diffusion equations with special nonlinearities. Of particular interest is the fact that the special first-order reduction is shown to give separatrices in appropriate phase spaces. An example of reaction-diffusion equation is presented without these special nonlinearities. While this equation is shown to have a special 'nonlinear' connection and resulting stability properties, it is intractable for either a singular manifold expansion of a first-order reduction. A Lie symmetry analysis is carried out, and it is shown that equations with continuous groups other than translational invariance are only a subclass of equations which are amenable to the special solution techniques. However, the 'rescaling ansatz' of Cariello and Tabor (1991) suggests that some symmetries are present.

Original languageEnglish (US)
Article number025
Pages (from-to)3773-3796
Number of pages24
JournalJournal of Physics A: Mathematical and General
Volume25
Issue number13
DOIs
StatePublished - 1992

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reaction-diffusion equations
Order Reduction
Reaction-diffusion Equations
First-order
nonlinearity
Nonlinearity
Nonlinear Connection
Lie Symmetry
Rescaling
Stability criteria
symmetry
Invariance
Stability Criteria
invariance
Phase Space
slopes
Symmetry
expansion

ASJC Scopus subject areas

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

Cite this

Non-generic connections corresponding to front solutions. / Powell, J.; Tabor, Michael.

In: Journal of Physics A: Mathematical and General, Vol. 25, No. 13, 025, 1992, p. 3773-3796.

Research output: Contribution to journalArticle

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