Help in hard model of RABR - solitons- solving PDE

[Johnbasko]

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

i will be gratefull for any help

 

[gtoguy97]

, thanks!</code>For the first equation, you can use a numerical method such as finite differences or finite volume. The main idea of these methods is to approximate the derivatives of the equation using finite difference operators. For the second equation, you can use a numerical method such as the Crank-Nicolson method. This is an implicit method which uses an implicit time discretization and a centered spatial discretization. You can find more information on this method here: https://en.wikipedia.org/wiki/Crank–Nicolson_method. Hope this helps!