Non-linear Schrodinger Equation (Differential Equation)

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Discussion Overview

The discussion revolves around simulating the nonlinear Schrödinger equation (NLS) for pulse propagation in optical fibers, specifically using the Finite Difference Time Domain (FDTD) method in MATLAB. Participants are exploring numerical solutions and methods for implementing the equation in their simulations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks assistance in simulating the nonlinear Schrödinger equation using the FDTD method, providing the equation's form and parameters involved.
  • Another participant suggests that an adaptive mesh type code is necessary, noting the complexity of solving the NLS equation, which is weakly nonlinear.
  • A request is made for MATLAB code related to the simulation, indicating a desire for direct assistance.
  • There is a clarification about the type of solution being sought, with one participant emphasizing the need for a time-dependent solution as opposed to traveling wave solutions.
  • A participant proposes a specific numerical solution involving generating a Gaussian pulse and propagating it along the fiber, detailing the form of the solution and the parameters used.
  • Another participant expresses doubt about the applicability of their code to the original request, reiterating the importance of adaptive mesh methods.
  • A request for guidance on adaptive mesh methods is made, along with a link to a Wikipedia page on the topic.

Areas of Agreement / Disagreement

Participants express differing focuses on the type of solutions (time-dependent vs. traveling wave) and the methods to be used (adaptive mesh vs. simpler numerical methods). The discussion remains unresolved regarding the best approach to take for the simulation.

Contextual Notes

Participants have not fully defined the assumptions or limitations of their proposed methods, and there is an absence of consensus on the most effective numerical approach for simulating the NLS equation.

syedmohsin
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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.
 
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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 traveling wave solutions.
 
hunt_mat said:
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.
 
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?
 
i don't understand the difference but yes i want time dependent solution
 
I look for a solution of the form A(t,x)=A(x-\omega t)
 
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
 
I don't think that my code will help you then but adaptive mesh will be the best way forward.
 
Can you guide me about adaptive mesh method or send some links about it?
 
  • #11
Thank you so much
 

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