Non-linear Schrodinger Equation (Differential Equation)

  • Thread starter syedmohsin
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  • #1
syedmohsin
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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

  • #2
hunt_mat
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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.
 
  • #3
syedmohsin
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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.
 
  • #4
hunt_mat
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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?
 
  • #5
syedmohsin
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i don't understand the difference but yes i want time dependent solution
 
  • #6
hunt_mat
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I look for a solution of the form [itex]A(t,x)=A(x-\omega t)[/itex]
 
  • #7
syedmohsin
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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
 
  • #8
hunt_mat
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I don't think that my code will help you then but adaptive mesh will be the best way forward.
 
  • #9
syedmohsin
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Can you guide me about adaptive mesh method or send some links about it?
 
  • #11
syedmohsin
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Thank you so much
 

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