In mathematics, the Bretherton equation is a nonlinear partial differential equation introduced by Francis Bretherton in 1964:
with p{\displaystyle p} integer and p≥2.{\displaystyle p\geq 2.} While ut,ux{\displaystyle u_{t},u_{x}} and uxx{\displaystyle u_{xx}} denote partial derivatives of the scalar field u(x,t).{\displaystyle u(x,t).}