Why Do Simulated and Theoretical Soliton Collisions Differ?

In summary, the conversation discusses the collision of two solitons of the NLS equation, with the goal of plotting out exact solutions from R.S. Johnson's book. The speaker has used MATLAB to produce a graph but it differs slightly from the one in the book. They also inquire about the availability of standard animations for this type of collision and ask for references. The conversation ends with a question about checking the input function and trying other packages for plotting.
  • #1
hanson
319
0
Hi all.
I am studying the collision of two solitons of the NLS equation.
Actually I just want to plot out the exact solutions given in R.S.Johnson's book. (page 321, figure 4.4).
I have used MATLAB to do this and produced the figure using exactly the same values for the parameters.
However, the produced graph is a little bit different from that in R.S.Johnson's book during collision.
I am wondering what's wrong.

Is there any standard animation available in the internet for the collision of two NLS solitons? This sounds very standard, but I can hardly find any...
Will you have any reference?
 
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  • #2
Did you check that the function which you input is in fact a solution of the NLS? Did you try plotting/checking it using another package such as Maple or Mathematica?
 
  • #3



Hello,

The collision of two NLS solitons is a complex and fascinating topic in nonlinear optics. It is not uncommon to see slight differences in the plots generated by different software programs, so it is possible that the discrepancy between your plot and R.S. Johnson's may be due to a difference in the numerical methods used.

I would suggest checking your code and parameters carefully to ensure that they match those used in the book. Also, it may be helpful to consult with other researchers or experts in this field to see if they have encountered similar issues and can provide guidance.

As for standard animations, there are a few available online, but they may not exactly match the specific parameters and conditions used in R.S. Johnson's book. However, they can still provide a visual representation of the collision process. I would recommend checking out resources such as the Nonlinear Optics Virtual Lab (https://www.geogebra.org/m/tq5pssk4) or the Nonlinear Schrödinger Equation Explorer (https://www.compadre.org/OSP/items/detail.cfm?ID=10272).

Additionally, you may find it helpful to consult other references on this topic, such as the paper "Soliton Collisions in the Nonlinear Schrödinger Equation" by M. A. Hoefer and D. M. J. T. Milson (https://arxiv.org/abs/nlin/0408038), which includes some animations and simulations of soliton collisions.

I hope this helps and wish you success in your studies. Good luck!
 

Related to Why Do Simulated and Theoretical Soliton Collisions Differ?

1. What is a Nonlinear Schrödinger (NLS) soliton?

A NLS soliton is a self-reinforcing wave packet solution of the one-dimensional nonlinear Schrödinger equation. It is characterized by its ability to maintain its shape and velocity while propagating without dispersion or dissipation.

2. How do two NLS solitons collide?

Two NLS solitons can collide when they are propagating in opposite directions along the same medium. This can occur in various physical systems, such as optical fibers, Bose-Einstein condensates, and water waves.

3. What happens when two NLS solitons collide?

When two NLS solitons collide, they undergo a complex interaction that can result in a variety of outcomes. These can include elastic scattering, inelastic scattering, fusion, and annihilation, depending on the initial conditions and parameters of the system.

4. Can collisions of NLS solitons be controlled or manipulated?

Yes, the outcome of NLS soliton collisions can be controlled or manipulated by adjusting the parameters of the system, such as the initial velocity and amplitude of the solitons. This can be achieved through experimental techniques or numerical simulations.

5. What applications do collisions of NLS solitons have?

Collisions of NLS solitons have applications in various fields, such as optical communications, quantum computing, and oceanography. They can be used to study and understand the behavior of nonlinear systems and to develop new technologies, such as all-optical switches and soliton-based data transmission.

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