I was reading Evans section 3.2. In it, he describes a way to solve the Cauchy problem using the method of Characteristics. The method seems to entail recasting a general first order pde, $F(Du,u,x)=0$, as an ODE of $2n+1$ variables, $F(p,u,x)=0$. Are there similar methods to obtain characteristics for general higher order PDEs? For instance, can't I just recast a 2nd order equation as a $4n+1$ ODE?