PRINCIPAL RESONANCES, LOCAL INTEGRABILITY AND CHAOS IN THE KOLMOGOROV-SPIEGEL-SIVASHINSKY EQUATION


UNAL G.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, vol.32, no.3, pp.455-472, 1994 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 3
  • Publication Date: 1994
  • Doi Number: 10.1016/0020-7225(94)90134-1
  • Title of Journal : INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
  • Page Numbers: pp.455-472

Abstract

A four-dimensional dynamical system which describes the travelling wave solutions of Kolmogorov-Spiegel-Sivashinsky (KSS) equation has been investigated by employing normal form analysis in the presence of principal resonances. The first two integrals of the normal form equations have been proven to exist for every order of the resonances when the wave celerity vanishes. Bifurcation values of the parameters are found analytically. With the aid of first integrals analytical solutions to a normal form equation in the presence of first principal resonance have been obtained. Moreover, the interaction between linear terms comprising the wave celerity and the periodic orbits in phase space yielding invariant tori has been observed in the numerical solutions. Deterministic chaos has been observed in Poincare surface of sections. The mechanism leading to chaos has also been discussed.