A LOCAL ANALYSIS OF THE KOLMOGOROV-SPIEGEL-SIVASHINSKY EQUATION


UNAL G., SUHUBI E.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, vol.30, no.5, pp.579-592, 1992 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 5
  • Publication Date: 1992
  • Doi Number: 10.1016/0020-7225(92)90004-z
  • Title of Journal : INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
  • Page Numbers: pp.579-592

Abstract

Kolmogorov-Spiegel-Sivashinsky (KSS) equation arises in different two dimensional viscous flows. Kolmogorov flow and the large-scale turbulent solar convection can be modelled by this equation [Los Alamos Sci. Spec. Iss. 218 (1987); Nucl. Phys. B (Proc. Suppl.) 2, 453 (1987)]. In this article, we have studied the group invariant solutions to the KSS equation. Also, a local analysis of the dynamical system obtained by the group theoretical means are performed by employing normal form analysis. This approach allowed us to obtain in analytical form an approximate travelling wave solution possessing periodic, quasi-periodic and aperiodic features. Bifurcations pertaining to the latter have been identified.