# Solving 4 coupled differential equation for modelling boson star

I'm trying to study about modelling star from a journal. To get the characteristics of the star, I have to solve 4 differential equations which are coupled each other. I want to use Mathematica 9 to solve this system of equations but I still can't do this simply. This is the system of equations:

$\lambda'=\frac{1-e^{\lambda}}{r}$+ $8\pi Gre^{\lambda}\left([m^2 +e^{-v}(\omega +qA)^2]\phi^2+ \frac{e^{-v-\lambda}{A'}^2}{2}+{\phi'}^2e^{-\lambda}]\right)$

$v'=\frac{-1+e^{\lambda}}{r}+8\pi Gre^{\lambda}\left([-m^2 +e^{-v}(\omega +qA)^2]\phi^2 - \frac{e^{-v-\lambda}{A'}^2}{2}+{\phi'}^2e^{-\lambda}\right)$

$A''+\left(\frac{2}{r}-\frac{v' + \lambda '}{2}\right)A'-2qe^{\lambda}\phi^2(\omega + qA)=0$

$\phi'' + \left(\frac{2}{r}+\frac{v' - \lambda '}{2}\right)\phi'+e^{\lambda}[(\omega+qA)^2 e^{-v}-m^2]\phi=0$

The boundary conditions are:

$\phi(\inf)=0, \phi'(\inf)=0, \phi(0)=constant, \phi'(0)=0$

$A(\inf)=0, A'(\inf)=0, A(0)=constant, A'(0)=0$

$v(\inf)=0, \lambda(0)=0$

Can someone tell me? That's journal just tell to use Mathematica and Runge-Kutta method.

• Does the function DSolve not do what you want, if you put in the four equations and the boundary conditions together? – Patrick Stevens Jul 16 '15 at 7:19
• @PatrickStevens DSolve is definitely not capable to solve these PDFs. I would say NDSolve is the only way. – funnyp0ny Jul 16 '15 at 9:18
• It would help others if you provided copy-pastable mathematica code of your system. – shrx Jul 16 '15 at 11:47