How can I solve this Second-Order Partial Differential Equation (PDE)?

Hello everyone,

I would like to know how can I solve a PDE in the form:

dE/dz + (a*i)(d^2(E)/dt^2) = i*b(1+i*c)*abs(E)^2*E - d*(1+i*f)*E - g*E

Where 'z' is a variable of distance,'t' is time and 'i' is imaginary. Then 'a,b,c,d,f and g' are constants. The equation is Parabolic, but I couldn't solve it with "pdepe" function because the kind of the equations they describe is second order with respect to dimension (z) and not time (t), and for what I've read they're not interchangeable.

Please let me know if you have an idea of how can I solve this, or the solver I should use. Thanks.