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I need your help to solve the following set of coupled differential equations numerically.

dn(t,z)/dt=I^5(t,z)+I(t,z)*n(t,z)

dI(t,z)/dz=I^5(t,z)-α(n(t,z))*I(t,z)

where I(t,0)=I0*exp(-4ln2(t/Δt)^2) and n(t,0)=0 and n(-certrain time,z)=0. Some constant parameters I did not show here.

α(n(t,z)) is just a parameter which depends linear on n(t,z)

I tried to solve it with Mathematica and NDsolve.. since it works fine if I just solve the first equation without the z dependence. But Mathematica seems to be unhappy with the boundary conditions.

Thanks!

Thomas