You'll want to change your form/submit button so that when clicked, it builds a url suitable for a GET request from the form parameters, and that consequently uses javascript to open a new window with that location.

This new url should point to your script, which generates the pdf and 'outputs' it.

The javascript should, after opening the new window, reset the form parameters for your next entry.

For openening the new window, have a look at W3 Schools