adding more text to a query string

On a site I am developing, I need a "special search" function. The search page is called with a search query from a form with _GET parameters like this : http://ift.tt/1M9EHqj

In the search page itself (where the result will be), how can I concatenate the s1 and s2 arguments so the results for wordpress would be treated as if it receives: http://ift.tt/1NgTX1y

Thanks for your help