Why Do Simulated and Theoretical Soliton Collisions Differ?

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hanson
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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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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?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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