Estevez–Mansfield–Clarkson equation

The Estevez–Mansfield–Clarkson equation is a nonlinear partial differential equation introduced by Pilar Estevez, Elizabeth Mansfield, and Peter Clarkson.^[1]

If U is a function of some other variables x, y, t, then we denote ${\displaystyle {\frac {\partial ^{3}U}{\partial t\,\partial y^{2}}}}$ by U_tyy, and so on. With that notation, the equation is

${\displaystyle U_{tyyy}+\beta U_{y}U_{yt}+\beta U_{yy}U_{t}+U_{tt}=0}$

in which ${\displaystyle U=u(x,y,t).}$