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Help in hard model of RABR - solitons- solving PDE

  1. Jan 19, 2009 #1
    hello all,

    im doing a research on model called RABR which supports dark and bright solitons.

    as first step i need to find numeric solution for the following equation:

    F'' = c1*F - c2*F/sqrt(c3+F^2)

    where c1, c2 , c3 are const, and F is function of x, i.e: F= F(x)

    i try to make finite differences, but it didnt work out.

    second model which is harder is the set of 2 equations:

    (1) dG^2/dt^2 - dG^2/dz^2 = c1*G + c2*i*P - 2*G*sqrt(1-abs(P)^2)

    (2) dP/dt = -i*P - G*sqrt(1-abs(P)^2)

    i dont know how to start simulate this, i thought about "crank nicolson" method, but im not sure it's fit, and how do i change the terms in this method

    i will be gratefull for any help
  2. jcsd
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