differential equation system with dz and dt variables

hello how to use split step Fourier method and rung kutta to solve differential equation system with dz and dt variable

[(d/dz) + (1/v_s)*(1/dt)+i*alpha_s*(d^2/dt^2)]*E_s(t,z)=((i*w_s*d_eff)/(n_s*c)) *E_p(t,z)*E'_p(t,z)*exp(i*deltak*z)

[(d/dz) + (1/v_i)*(1/dt)+i*alpha_i*(d^2/dt^2)]*E_i(t,z)=((i*w_i*d_eff)/(n_i*c)) *E_p(t,z)*E'_s(t,z)*exp(i*deltak*z)

[(d/dz) + (1/v_p)*(1/dt)+i*alpha_p*(d^2/dt^2)]*E_p(t,z)=((i*w_p*d_eff)/(n_p*c)) *E_i(t,z)*E'_s(t,z)*exp(-i*deltak*z)