Mathematica PDE Plot Mathematica(Multivalue)

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The discussion centers on plotting the implicit solution to the partial differential equation (PDE) defined by u(x,y) = sin(x - t u(x,y)). The original poster expresses uncertainty about how to approach this task, noting previous experience with similar equations but lacking clarity on the current one. There's skepticism about the effectiveness of parameterization due to the presence of the u(x,y) term, which complicates the plotting process. The conversation highlights the challenges of visualizing implicit solutions in PDEs and the difficulties in isolating u(x,y) for plotting purposes.
Winzer
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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.
 
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Nothing?
I don't suppose parameterizing would help, I would still have the u(x,y) term i think.
 

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