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Numerical Schemes for KdVs?

  1. Nov 3, 2009 #1

    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?
  2. jcsd
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