Solving a system of PDE with a nonlinear term

Hello everyone

I have a system of PDE with a nonlinear term that I need to solve. Can anyone help me to solve this equation using matlab in terms of space (z) and time (t) and get u(z,t), v(z,t) and w(z,t). Thanks in advance for your time.

the parameters are as follows

Nt = 1024; T = 50; dt = T/Nt;

t = (-Nt/2:1:Nt/2-1)'*dt;

dw = 2*pi/T; w = [0:Nt/2-1 0 -Nt/2+1:-1]'*dw;

Z = 2; (Total Length)

delta0 = 0.2; delta1 = 0.2; delta2 = 0.2;

tau = 0.1;

gamma = 4; beta2 = -2;

mshape = 3;

chirp0 = 0.25;

C = 0.1;

g(z) = 0.4*z

u0 = 0.25*exp(-(t/5).^2);

v0 = sech(t) .* exp(-0.5i * chirp0 * t .^ 2);

w0 = exp(-0.5 * (1 + 1i * chirp0) .* t .^ (2 * mshape));