# 4.3.6. pde.pdes.kuramoto_sivashinsky module

The Kardar–Parisi–Zhang (KPZ) equation describing the evolution of an interface

class KuramotoSivashinskyPDE(nu=1, *, noise=0, bc='auto_periodic_neumann', bc_lap=None)[source]

Bases: PDEBase

The Kuramoto-Sivashinsky equation

The mathematical definition is

$\partial_t u = -\nu \nabla^4 u - \nabla^2 u - \frac{1}{2} \left(\nabla h\right)^2 + \eta(\boldsymbol r, t)$

where $$u$$ is the height of the interface in Monge parameterization. The dynamics are governed by the parameters $$\nu$$ , while $$\eta$$ is Gaussian white noise, whose strength is controlled by the noise argument.

Parameters:
diagnostics: Dict[str, Any]

Diagnostic information (available after the PDE has been solved)

Type:

dict

evolution_rate(state, t=0)[source]

evaluate the right hand side of the PDE

Parameters:
• state (ScalarField) – The scalar field describing the concentration distribution

• t (float) – The current time point

Returns:

Scalar field describing the evolution rate of the PDE

Return type:

ScalarField

explicit_time_dependence: bool | None = False

Flag indicating whether the right hand side of the PDE has an explicit time dependence.

Type:

bool

property expression: str

the expression of the right hand side of this PDE

Type:

str