Series solution to coupled nonlinear ODEs

1. Mar 2, 2006

daso

Hi,

I have a system of three coupled nonlinear ODEs:

$$\frac{d}{du}(nu)=exp(-\phi),$$

$$u\frac{du}{dx}=\frac{d\phi}{dx}-\frac{u}{n}exp(-\phi),$$

$$\frac{d^2 \phi}{dx^2}=n-exp(-\phi),$$

with boundary conditions

$$\phi=\phi'=u=n=0 \text{ at } x=0$$

Does anyone know, or have references to, how to solve these with a series expansion? I am only interested in the solution for $$x \ll 1$$, so higher order terms can be neglected.

Thankful for any help!

/Daniel