Kuramoto–Sivashinsky equation

In mathematics, the Kuramoto–Sivashinsky equation (also called the KS equation) is a partial differential equation used to model complex patterns and chaotic behavior in physical systems. It is one of the simplest PDEs known to exhibit chaos. The fourth-order equation was first derived in the late 1970s by Yoshiki Kuramoto and Gregory Sivashinsky to describe the instabilities of a laminar flame front. It has since been found to apply to other systems, such as the flow of a thin liquid film down an inclined plane and trapped-ion instability in plasmas.

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