A local analysis of the Kolmogorov-Spiegel-Sivashinsky equation

Abstract

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.