<< RealTime3D`

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

fa[x_]  :=  
        e[x - x0,  .05]  +   .37  e[x - x0 -  .09,  .055];
f[x_]  :=  fa[x]  -  fa[-x];

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

\(\(\(x0\  = \  .4\)\(;\)\(\ \)\(δt\  = \  .01\)\(;\)\(\ \)\(\(Plot[u[#, x], {x, 0, 1.5}, PlotRange\  -> {\(-1.2\), 1.2}, 
          AspectRatio ->  .5, 
          PlotStyle\  -> \ {Thickness[ .004], 
              Hue[ .05]}] &\)\  /@ 
\((	\ Range[0, 
          2, δt])\)\)\(;\)\(
\)\(
\)\(
\)\)\)