Competition between generic and nongeneric fronts in envelope equations

James A. Powell, Alan C Newell, Christopher K R T Jones

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

Arguments are presented for understanding the selection of the speed and the nature of the fronts that join stable and unstable states on the supercritical side of first-order phase transitions. It is suggested that from compact support, nonpositive-definite initial conditions, observable front behavior occurs only when the asymptotic spatial structure of a trajectory in the Galilean ordinary differential equation (ODE) corresponds to the most unstable temporal mode in the governing partial differential equation (PDE). This selection criterion distinguishes between a nonlinear front, which has its origin in the first-order nature of the bifurcation, and a linear front. The nonlinear front has special properties as a strongly heteroclinic trajectory in the ODE and as an integrable trajectory in the PDE. Many of the characteristics of the linear front are obtained from a steepest-descent linear analysis originally due to Kolmogorov, Petrovsky, and Piscounov [Bull. Univ. Moscow, Ser. Int., Sec. A 1, 1 (1937)]. Its connection with global stability arguments, and in particular with arguments based on a Lyapunov functional where it exists, is pursued. Finally, the point of view and results are compared and contrasted with those of van Saarloos [Phys. Rev. A 37, 211 (1988); 39, 6367 (1989)].

Original languageEnglish (US)
Pages (from-to)3636-3652
Number of pages17
JournalPhysical Review A
Volume44
Issue number6
DOIs
StatePublished - 1991

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envelopes
trajectories
partial differential equations
differential equations
Moscow
descent

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Competition between generic and nongeneric fronts in envelope equations. / Powell, James A.; Newell, Alan C; Jones, Christopher K R T.

In: Physical Review A, Vol. 44, No. 6, 1991, p. 3636-3652.

Research output: Contribution to journalArticle

Powell, James A. ; Newell, Alan C ; Jones, Christopher K R T. / Competition between generic and nongeneric fronts in envelope equations. In: Physical Review A. 1991 ; Vol. 44, No. 6. pp. 3636-3652.
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