Solution of the Burgers equation using an implicit linearizing transformation

The initial-boundary-value problem on the semi-infinite interval and on a finite interval for the Burgers equation ut = uxx + 2uxu is solved using a stream function ∅ and a linearizing transformation w = e∅. The transformation reduces the equation to a heat equation with appropriate initial and homogeneous time-dependent linear boundary conditions. One advantage of this method is that we never need to find an explicit expression for ∅ in our computations.