Kuramoto-Sivashinsky Equation

Note

For the Kuramoto-Sivashinsky equation there are six different Orbit subclasses

Which orbit class should I use?

Let \(G\) denote a group of discrete spatiotemporal symmetries \(G = \{e, \sigma, \tau, \sigma\tau\}\) which represent the identity, spatial reflection, half-period time translation and spatiotemporal shift reflection (glide) which is the composition of spatial reflection and half-period time translation.

Orbit Class	Invariance	Equivariance
OrbitKS	None	Discrete rotations
RelativeOrbitKS	None	Discrete rotations
RelativeEquilibriumOrbitKS	None	Discrete rotations
ShiftReflectionOrbitKS	Spatial reflection + half-period time translation	\(G\)
AntisymmetricOrbitKS	Spatial reflection	\(G\)
EquilibriumOrbitKS	Spatial Reflection and time translation	\(G\)

Orbit Types

• OrbitKS
• RelativeOrbitKS
• AntisymmetricOrbitKS
• EquilibriumOrbitKS
• RelativeEquilibriumOrbitKS
• ShiftReflectionOrbitKS

Utilities

• Kuramoto-Sivashinsky Utilities