Hello, every experts!

I want to know how to programming a mathematica notebook to generate the result in the paper arXiv: 1404.7133, where the authors said that using a numerical shooting method and matching the two expansions (2.17), (2.18) in the paper as two boundary conditions, then we can get the Fig. 1 and the values (2.19) in the paper. I don't have good ideas on realizing their result for sometime. Could you tell me some useful suggestions on this problem? Thank you very much!

The paper can be found on the website http://arxiv.org/abs/1404.7133

Best regards , Xu