m = (E^(-(d[t]^2/(a[t]^2 + 1))))/(a[t]^2 + 1)^(5/2)
n = Sqrt[[Pi]]

NDSolve[{c'[
t] == (2*
m)*(2*(a[t]^4*b[t] - 2*a[t]^2*b[t]*d[t]^2 + a[t]^2*b[t] +
     a[t]^2*d[t]*c[t] + d[t]*c[t]) - a[t]^2*d[t]*-1),
        d'[t] == (a[t]^2*2*m*(a[t]^2 - 2*d[t]^2 + 1)) + c[t] ,
   a'[t] == a[t]*(1 + a[t]^2)^-1*d[t]*2*
 m*(-2*a[t]^4 + 2*a[t]^2*d[t]^2 - a[t]^2 + 1) + 2*a[t]*b[t],
 b'[t] == 1/(2 a[t]^4) - n/(2*Sqrt[2 [Pi]]*a[t]^3) +
 1*m (a[t]^2 + 2*d[t]^2 + 1) - 2*b[t]^2, c[0] == 0.25,
 d[0] == -12, a[0] == 1.0, b[0] == 0}, {d, c, a, b}, {t, 0, 120}]