Buckmaster equation

In mathematics, the Buckmaster equation is a second-order nonlinear partial differential equation, named after John D. Buckmaster, who derived the equation in 1977.^[1] The equation models the surface of a thin sheet of viscous liquid. The equation was derived earlier by S. H. Smith and by P Smith,^[2][3] but these earlier derivations focused on the steady version of the equation.

The Buckmaster equation is

${\displaystyle u_{t}=(u^{4})_{xx}+\lambda (u^{3})_{x}}$

where ${\displaystyle \lambda }$ is a known parameter.