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## Main Question or Discussion Point

I have to solve the following coupled differential equations

d^2f(r)/dr^2+1/r*df(r)/dr+(2-2*f(r)^2-2*a*g(r)^2-l_1^2/r^2)*f(r)=0

d^2g(r)/dr^2+1/r*dg(r)/dr+(2-2*g(r)^2-2*a*f(r)^2-l_2^2/r^2)*g(r)=0,

where a is the coupling. I think that it is not possible to solve it analytically (even in case a==0), so i have to do it numerically. I tried it with matlab, but bvp4c can not solve equations with singularities of second kind. Can somebody help me? (I'm a advanced user of matlab)

d^2f(r)/dr^2+1/r*df(r)/dr+(2-2*f(r)^2-2*a*g(r)^2-l_1^2/r^2)*f(r)=0

d^2g(r)/dr^2+1/r*dg(r)/dr+(2-2*g(r)^2-2*a*f(r)^2-l_2^2/r^2)*g(r)=0,

where a is the coupling. I think that it is not possible to solve it analytically (even in case a==0), so i have to do it numerically. I tried it with matlab, but bvp4c can not solve equations with singularities of second kind. Can somebody help me? (I'm a advanced user of matlab)