Estevez–Mansfield–Clarkson equation

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

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


 * $$ U_{tyyy}+\beta U_y U_{yt}+\beta U_{yy} U_t+U_{tt}=0$$

in which $$U=u(x,y,t).$$