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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

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# Help in hard model of RABR - solitons- solving PDE

Can you offer guidance or do you also need help?

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