<< RealTime3D`

e[x_, a_]  :=  (E^(-(x/a)^2))

x0  =  - .7; 
    f[x_]  :=  e[x - x0,  .05]  +   .37  e[x - x0 -  .19,  .055]; 
    u[t_, x_] :=  f[x  - t]

Plot3D[u[t, x], {x, -1, 1}, {t, 0, 1.8}, 
      BoxRatios  -> {1, 1,  .2}, Boxed -> False, 
      Axes -> False, Mesh -> False, 
      PlotPoints -> 150]

\(\(\(\ \)\(\(δt\  = \  .02\)\(;\)\(\ \)\(\(Plot[
          u[#, x], {x, \(-1\), 1}, PlotRange\  -> {\(- .2\), 1.2}, 
          AspectRatio\  -> \  .3, 
          PlotStyle\  -> \ {Thickness[ .004], Hue[ .75]}] &\)\  /@ 
\ 
      Range[0, 1.8, δt]\)\(;\)\(
\)\(
\)\(
\)\)\)\)