text: The 1d version of the Kuramoto–Sivashinsky equation is
  An alternate form is
  obtained by differentiating with respect to  and substituting . This is the form used in fluid dynamics applications.
  The Kuramoto–Sivashinsky equation can also be generalized to higher dimensions. In spatially periodic domains, one possibility is
  where  is the Laplace operator, and  is the biharmonic operator.