System of First-Order Quasilinear PDEs: Burgers' Equation

The Burgers' equation is given by $u_{t}+uu_{x}=\nu u_{xx}$, where $u=u(x,t)$ and $\nu$ is the kinematic viscosity.

How do I rewrite the equation (or any higher order PDE) as a system of first-order quasilinear PDEs? I am particularly interested in a general methodology. Books or online materials that discuss this in detail will be appreciated.

• Try the transformation $u = -2\nu\frac{\partial \log F}{\partial x}$ under which the equation transforms into the linear diffusion equation $\frac{\partial F}{\partial t} = \nu \frac{\partial^2 F}{\partial x^2}$ (modulo a integration constant). – Winther Aug 18 '14 at 14:43