Growth shapes and pulses in a generalized Kuramoto-Sivashinsky equation

We examine the growth shapes that arise as solutions to a generalized Kuramoto-Sivashinsky equation, when a small perturbation expands into a linearly unstable uniform flat regime. We show how, by including both the linear instabilities and the coherent structures, i.e. pulses, the growth shapes can be predicted for a large range of parameters. 1 Introduction We study the growth shapes which appear when a small localized perturbation expands into an unstable uniform medium. There are many examples of deterministic growth, i.e. growth where noise plays no role. These examples include propagating flames fronts [1], chemical turbulence [2] and localized turbulent spots in pipe flows or boundary layers [3]. To study these growth phenomena, we study a generalized version of the Kuramoto-Sivashinsky equation. The equation has been derived in a number of different physical contexts including chemical turbulence [4], surface waves [5] and flame fronts [6]. 2 The Generalized Kuramoto-Sivashi..