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Non-linear Schrodinger Equation (Differential Equation)

  1. Aug 13, 2011 #1
    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.
     
  2. jcsd
  3. Aug 14, 2011 #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.
     
  4. Aug 14, 2011 #3

    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.
     
  5. Aug 14, 2011 #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?
     
  6. Aug 14, 2011 #5
    i don't understand the difference but yes i want time dependent solution
     
  7. Aug 14, 2011 #6

    hunt_mat

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    I look for a solution of the form [itex]A(t,x)=A(x-\omega t)[/itex]
     
  8. Aug 14, 2011 #7
    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
     
  9. Aug 14, 2011 #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.
     
  10. Aug 14, 2011 #9
    Can you guide me about adaptive mesh method or send some links about it?
     
  11. Aug 14, 2011 #10

    hunt_mat

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  12. Aug 14, 2011 #11
    Thank you so much
     
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