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.

I have started with putting the whole expression in like this 
$\frac{\partial (f(x-ct,t)+c)}{\partial t}+f(x,t) \frac{\partial (f(x-ct,t)+c)}{\partial x}+\frac{\partial (f(x-ct,t)+c)^3}{\partial^3 x}$  and then get $(-c,0)+(f(x-ct)+c)+(1,0) +0$ but it doesn't seme right?
