In mathematics, the Buckmaster equation is a second-order nonlinear partial differential equation, named after John D. Buckmaster, who derived the equation in 1977.Buckmaster, J. (1977). Viscous sheets advancing over dry beds. Journal of Fluid Mechanics, 81(4), 735–756. 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,Smith, S. H. (1969). A non-linear analysis of steady surface waves on a thin sheet of viscous liquid flowing down an incline. Journal of Engineering Mathematics, 3(3), 173–179.Smith, P. (1969). On steady long waves on a viscous liquid at small Reynolds number. Journal of Engineering Mathematics, 3(3), 181–187. but these earlier derivations focused on the steady version of the equation.
The Buckmaster equation is
where is a known parameter.
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