Derivation of Burgers' Equation

Question

I'm aware that it is possible to reduce Navier-Stokes to Burgers by neglecting pressure, and that one can derive the inviscid form by considering an ideal gas and concluding that the convective acceleration is zero. My question is whether there is a way to extend the second example to include kinematic viscosity $\nu$, i.e. to derive $$ \frac{\partial u}{\partial t} + u\cdot \nabla u = \nu\nabla^2 u $$ in one dimension. I came across an exercise in James Haberman's "Applied Partial Differential Equations" but think I lack the prerequisites to tackle it. Any references or suggestions would be greatly appreciated.

Answer 1

Professor Falkovich seems to provide a general derivation for Berger's equation starting from Navier-Stokes equation at about 19:00 in http://scgp.stonybrook.edu/video_portal/video.php?id=3160 Although it's not clear to me yet what exactly $u$ corresponds to in the end.