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I am working with the DE

[tex] u_t + u_{xxx} + u^su_x = 0 [/tex]

where s>0 is any real number.

I am trying to simulate the collision of two travelling solitons numerically (something like this: http://www.tu-chemnitz.de/physik/KSND/abb/anim.gif), using a finite-difference scheme, but my numerical solutions either blow up or do something crazy.

I used the initial conditions

[tex]f(x) = e^{-x^2}[/tex]

and then 10*f(x-10)+f(x+10) or something like that to get two solitons with different velocities. Any help?

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# Numerical Schemes for KdVs?

Can you offer guidance or do you also need help?

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