# 4.3.9. pde.pdes.swift_hohenberg module

The Swift-Hohenberg equation

class SwiftHohenbergPDE(rate=0.1, kc2=1.0, delta=1.0, *, bc='auto_periodic_neumann', bc_lap=None)[source]

Bases: PDEBase

The Swift-Hohenberg equation

The mathematical definition is

$\partial_t c = \left[\epsilon - \left(k_c^2 + \nabla^2\right)^2\right] c + \delta \, c^2 - c^3$

where $$c$$ is a scalar field and $$\epsilon$$, $$k_c^2$$, and $$\delta$$ are parameters of the equation.

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