<< RealTime3D`

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

f[x_]  :=  
        e[x -  .5,  .05]  +  .5 e[x  +   .3,  .08];

u[t_, x_]  :=  ((f[x  -  t]  +  f[x  +  t])/2)

Plot3D[u[t, x], {x, -1, 1}, {t, 0, 1.5}, 
      BoxRatios  -> {1, 1,  .2}, Boxed -> False, 
      Axes -> False, Mesh -> False, 
      PlotPoints -> 250]

\(\(\(\ \)\(δt\  = \  .01; \ \(Plot[u[#, x], {x, \(-1\), 1}, 
          PlotRange\  -> {\(-1.2\), 1.2}, 
          PlotStyle\  -> \ {Thickness[ .004], 
              Hue[ .55]}] &\)\  /@ 
\((	\ Range[0, 
          2, δt])\);\)\)\)