with(plots):
w1:=3*exp(-(x-t)^2);
P:=animate(w1,x=0..2*Pi,t=0..3*Pi,frames=75): display(P,insequence=true);
w2:=-3*exp(-(x+(t-3*Pi))^2);
Q:=animate(w2,x=0..2*Pi,t=0..3*Pi,frames=75): display(Q,insequence=true);
wsum:=w1+w2;
R:=animate(wsum,x=-Pi/4..3*Pi,t=0..3*Pi,frames=75): display(R,insequence=true);