# Non-linear Schrodinger Equation (Differential Equation)

syedmohsin
Hello,

i am working on pulse propagation in optical fiber. i have to simulate the nonlinear Schrodinger equation using the FDTD (Finite Difference Time Domain) method. The Schrodinger equation has the form dA/dz = i/2 β2 d2A/dt2 –α/2 +iγ |A2|A

where β2 is dispersion, α is attenuation and γ is fiber non-linearity.

I need to do this in MATLAB. Please help me in simulation or send me a MATLAB code related to it.

## Answers and Replies

Homework Helper
You will need an adaptive mesh type code. The NLS equation is weakly nonlinear but the equations are somewhat tricky to solve, I have written programs which find travelling wave solutions.

syedmohsin
You will need an adaptive mesh type code. The NLS equation is weakly nonlinear but the equations are somewhat tricky to solve, I have written programs which find travelling wave solutions.

Sir can you email main that code? my email is syedmohsinshah@gmail.com
If you give me some time i will discuss my work with you by email.

Homework Helper
I am looking for travelling wave solutions, and I think that is a vast difference to what you want. You want time dependent one right?

syedmohsin
i don't understand the difference but yes i want time dependent solution

Homework Helper
I look for a solution of the form $A(t,x)=A(x-\omega t)$

syedmohsin
For my work i have a simple numerical solution. i need to generate a Gaussian pulse and then to propagate along the fiber length. i can use simple difference derivative or Crank Nicholson difference. The solution has the form:
Ai+1,n = Ai,n +j delta x ( ½ β2(Ai,n+1 – 2Ai,n + Ai,n-1)/delta t2 ) j delta x γ |A2|A

Where β2 is fiber dispersion and γ is fiber nonlinearity
i is space step and n is time step

Homework Helper
I don't think that my code will help you then but adaptive mesh will be the best way forward.

syedmohsin
Can you guide me about adaptive mesh method or send some links about it?

Homework Helper
syedmohsin
Thank you so much