Optical Solitons - General understanding and Project ideas

1. Jan 6, 2010

Hard Maths

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,

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. Jan 7, 2010

Manman

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?

3. Jan 9, 2010

Manman

Please can someone help me out, i'm really struggling!