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,[1] named after Yoshiki Kuramoto[2] and Gregory Sivashinsky, who derived the equation to model the diffusive instabilities in a laminar flame front in the late 1970s.[3][4] The equation reads as

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

where is the Laplace operator and its square, is the biharmonic operator. The Kuramoto–Sivashinsky equation is known for its chaotic behavior.

See also

References

  1. Weisstein, Eric W. "Kuramoto-Sivashinsky Equation". MathWorld. Wolfram Research.
  2. Kuramoto, Y. (1978). Diffusion-induced chaos in reaction systems. Progress of Theoretical Physics Supplement, 64, 346-367.
  3. Sivashinsky, G. S. (1977). Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations. In Dynamics of Curved Fronts (pp. 459-488).
  4. Sivashinsky, G. I. (1980). "On flame propagation under conditions of stoichiometry". SIAM Journal on Applied Mathematics. 39 (1): 67–82. doi:10.1137/0139007.


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