u[x_, t_, k0_, a_]:=
1/Sqrt[1+a*2*I*t]*Exp[-1/4*k0^2]*Exp[-1/(4*a+I*2*t)*(x-I*k0/2)^2]
v[x_, t_, w_, k_]:=
Cos[k*x-w*t]
Animate[Manipulate[Plot[{Abs[u[x, t, k0, a]]*v[x, t, w, k],Abs[u[x, t, k0, a]]},  {x, -60, 60},Axes->{True, False}, PlotRange->{-2, 2}, PlotStyle->Thick, PlotLegends->{"Wave Packet", "Amplitude"}] ,{{k, 1, "Frequency"}, 0, 5},  {{k0, 0, "Group Velocity"}, -3, 3}, {{w, 0, "Phase Velocity"}, -5, 5},{{a, .5, "Dispersion Rate"}, .1, 2}],  {{t, 0, "Time"}, 0, 10}]