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.
Thanks, Radz.