PDE Plot Mathematica(Multivalue)

[Winzer]

I am trying to plot:
u(x,y)=sin(x-t u(x,y))
An implicit solution to a PDE.
I have no clue how to do this; I've plotted an equation like this before.

 

[Winzer]

Nothing?
I don't suppose parameterizing would help, I would still have the u(x,y) term i think.