eqns = {D[g[z, t], z] == (1/vg)(ML -(r0^2/(Rd^2f[z,t]^3))+M(1+Rn(r/r0)^2)a^2/((1+Xg[z,t]/f[z,t]^2)^(3/2)))(D[g[z, t], t]-((2g[z,t]/f[z,t])D[f[z,t],t]))-((4g[z,t]r0^2)/(Rd^2f[z,t]^3))D[f[z,t],t], D[f[z, t], z, z] ==( 1/(Rd^2f[z,t]^3))-((2MRn)/r0^2)f[z,t]-((MX)/(r0^2f[z,t]^3))(g[z,t]/((1+Xg[z,t]/f[z,t]^2)^(3/2)))}
bcs = {g[0,t]==Exp[-t^2],f[0,t]==1,f[1,t]==1,Derivative[1, 0][f][0, t] ==0};
ics = {g[z,0]==1,f[z,0]==1 };
sol = NDSolveValue[{eqns, bcs, ics}, {g, f}, {z, 0, 10^-6}, {t, 0, 3*10^-15}, Method -> {"IndexReduction" -> Automatic, "EquationSimplification" -> "Residual", "PDEDiscretization" -> {"MethodOfLines", "SpatialDiscretization" -> {"TensorProductGrid", "MinPoints" -> 50, "MaxPoints" -> 50}}}]
vg, M , L r0, Rd, Rn, X are constants.
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