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Homework Help: Optical Solitons - General understanding and Project ideas

  1. Jan 6, 2010 #1
    1. The problem statement, all variables and given/known data

    I have written a working program that can obtain a numerical solution to the nonlinear Schrodinger equation, given at initial pulse, using the split-step Fourier method.

    I have performed the first task of writing a working programme and have shown that if the initial pulse is sech(x) then there is no change over time and if i try 3sech(x) then the pulse changes but returns to the initial profile at t=pi/2.

    Below is the next stage of the project,

    2v1q137.jpg



    3. The attempt at a solution

    I have tried first and 3rd point and obtained results, but nothing i can really write a project on.

    I have a pile of books on solitons, i have spent days researching on the internet and i still have no good ideas that will make for a decent project, i really need some help on this.
     
  2. jcsd
  3. Jan 7, 2010 #2
    If this is asking too much, maybe someone can help me with some simpler more focussed questions.

    For something to be a soliton solution, does it have to be sech shape and does it have have to repeat?

    I know that 3sech(x) has a period of pi/2 but 1.5sech(x) has no period that i can see, so this must mean that not all sech(x) pulses can be soliton solutions, only ones with a certain amplitude, is this right?

    (i am meant to be able to show how the gaussian pulse evolves into a fundamental solition)
    I have found that the Gaussian pulse becomes a sech shape at a time of 1.5 but after this point, no periodicity occurs, nor does it remain a sech shape, can someone shed some light on this, is this a correct result?
     
  4. Jan 9, 2010 #3
    Please can someone help me out, i'm really struggling!
     
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