Kuramoto–Sivashinsky equation

A spatiotemporal plot of a simulation of the Kuramoto–Sivashinsky equation

In mathematics, the Kuramoto–Sivashinsky equation (also called the KS equation or flame equation) is a fourth-order nonlinear partial differential equation, named after Yoshiki Kuramoto and Gregory Sivashinsky, who derived the equation to model the diffusive instabilities in a laminar flame front in the late 1970s. The equation reads as

$u_{t}+\nabla ^{4}u+\nabla ^{2}u+{\frac {1}{2}}|\nabla u|^{2}=0,$

where $\nabla ^{2}$ is the Laplace operator and its square, $\nabla ^{4}$ is the biharmonic operator. The Kuramoto–Sivashinsky equation is known for its chaotic behavior.

See also

• Clarke's equation