InitCond[x_] = 
      Exp[-x^2]

    FluxFunc[u_] = u

    WaveSpeed[x_] =  FluxFunc'[InitCond[x]]
  

    ParametricPlot3D[{x + t*WaveSpeed[x], InitCond[x], t}, {x, -3, 
        3}, {t, 0, 3}, Boxed -> False,  Axes ->  False, 
      Background -> GrayLevel[0], 
      DefaultColor -> RGBColor[1, 0, 0], 
      ImageSize -> {550, 400}]