Broer–Kaup equations

The Broer–Kaup equations are a set of two coupled nonlinear partial differential equations:^[1]

${\displaystyle u_{y,t}+(2uu_{x})_{x}+2v_{xx}-u_{xxy}=0}$

${\displaystyle v_{t}+2(vu)_{x}+v_{xx}=0}$