<< 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, -8, 8}];
f[x_]  :=  fa[x]  -  fa[-x];

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

\(x0\  = \  .3; \ δt\  = \  .01; \ \(Plot[u[#, x], {x, \(-4\), 4}, 
          PlotRange\  -> {\(-1.2\), 1.2}, AspectRatio ->  .15, 
          PlotStyle\  -> \ {Thickness[ .004], 
              Hue[ .05]}] &\)\  /@ 
\((	\ Range[0, 
          2, δt])\);\)