Non-linear Schrodinger Equation (Differential Equation)

[syedmohsin]

Hello,

i am working on pulse propagation in optical fiber. i have to simulate the nonlinear Schrödinger equation using the FDTD (Finite Difference Time Domain) method. The Schrödinger 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.

 

[hunt_mat]

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 traveling 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 traveling 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.

 

[hunt_mat]

I am looking for traveling 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

 

[hunt_mat]

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

 

[hunt_mat]

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?

 

[hunt_mat]

http://en.wikipedia.org/wiki/Adaptive_mesh_refinement

 

[syedmohsin]

Thank you so much