<< RealTime3D`

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

fa[x_]  :=  
        Sum[ e[x - x0 - 2 k,  .05]  +   .37  e[
                x - x0 - 2 k -  .09,  .055] , {k, -2, 2}];
f[x_]  :=  fa[x]  -  fa[-x];

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

x0  =   .3; 
    Plot3D[u[t, x], {x, 0, 1}, {t, 0, 2.7}, 
      BoxRatios  -> { .5, 1,  .3}, Boxed -> False, 
      Axes -> False, Mesh -> False, 
      PlotPoints -> 150]

\(x0\  = \  .3; \ δt\  = \  .01; \ \(Plot[u[#, x], {x, 0, 1}, 
          PlotRange\  -> {\(-1.2\), 1.2}, 
          PlotStyle\  -> \ {Thickness[ .004], 
              Hue[ .75]}] &\)\  /@ 
\((	\ Range[0, 
          2, δt])\);\)