Question regarding a PDE I can see where to start on a $f(x,t)$ that solves a PDE $f_t+f*f_x+f_{xxx}=0$, then to show that it will also be true for $f(x-ct,t)+c$ for any number $c$
I can't see where to start on a problem. If a function $f(x,t)$ solves the PDE 
$$f_t + f f_x + f_{xxx} = 0$$
I want to show that $f(x-ct,t)+c$, for any number $c$, also solves the PDE.

With the chain rule I get $X(x)T'(t)+X(x)T(t)X'(x)T(t)+X'''(x)T(t)=0$
with $X(x)=x-ct$ and $T(t)=t$, where would $+c$ go? 
