I am examining the equation
$ u_t + u_x + u^2 u_x + u_{xxx} = 0 $
It seems that through a change of variables this equation can be reduced to
$ v_{t'} + v^2 v_y + v_{yyy} = 0 $
But I dont understand how this is done. Can anyone point me in the right direction?
Make the change of variable $x\to x+t$ and define $v(t,x)=u(t,x+t)$.