# Characteristic Methods for N-order PDEs

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?

• There is a method that is outlined in Evan’s PDE that works, but I wouldn’t say it all that enlightening. – DaveNine Dec 24 '17 at 17:30
• You can try, but you won't get a closed system of characteristic ODEs for second or higher order PDEs. The method of characteristics is generally only applicable to first order equations. – Jeff Dec 24 '17 at 17:53
• @DaveNine The method of characteristics in Evans book is for first order PDEs. – Jeff Dec 24 '17 at 17:54