On the next
page? That is, the page is reloaded? What is that jquery you have... maybe still we are talking about PHP?
In the General case — it is not necessary to take anything from the URL. You already sent a GET request, and received in return some data which brought on next page.
Now take your get, take out the queries you want and insert it back into shape. If you do PHP, then do as stated in the first comments, just in case to check:
<input type="text" name="name" value="'.($_GET['name'] ? $_GET['name'] : ").'">
If you have a JS/JQ, meaning exactly the same, only rewrite for themselves.