non-linear elliptic differential equation

Questions
, ,
1

Hi all, I am having hard time in solving the following non-linear elliptic equation numerically for u:

(\eta+u) \bigg((\eta+u)^2 -\frac{\varphi ^2}{4} \bigg)\nabla^2 u -\frac{\varphi^2}{4} \partial _m \bigg ( \frac{\eta+u-1}{ \varphi} \bigg) \times \partial ^m \bigg ( \frac{\eta+u+1}{ \varphi} \bigg) = 0

This is (3.31) equation of the following paper: http://arxiv.org/pdf/0907.1151v2.pdf

I tried to edit it. Hope this is the convenient form.

2

Could you please make the equation readable using this post How to post and use Wolfram Community , especially using the Plain Text of the equation from a Mma notebook. The equation seemingly still has not been converted to Mma syntax. If you want to display it straight in LaTeX form, this should be nowadays possible using the above link too. Any boundary conditions?

3

Thanks Udo for the suggestion, I made corrections now. The equation that I am struggling to code, is from the above paper. It takes u function 1 at infinity.