Improving full ajax website

I would like to try to improve a script that I use to make my ajax site. But after several attempts, no results. I need some help! ^^

This script was found on GitHub, and the author left a simple demo page. The author uses history.js. HERE

Here's the problem: 1- The back button works normally, but do not work when you have to return to the "index.php".

2- I would change the name of the created pages, but I can not win without breaking the script.

3- Finally I would like to add a function to load the div and use jqueryscrollto to make a transition effect.

I originally wanted to use this script (http://ift.tt/1lrQjVG) but I have not managed to implement. Having no single demo page using this script.

Thank you in advance if you look at the problem.