Author archive rewrite problem

I have the following website in which I can access the author archive page with the complete string URL i.e. http://mydomain.net/author/peter but when I click on a link that has peter’s id such as http://mydomain.net/?author=21 then the link does not get rewritten to http://mydomain.net/author/peter.

How can I achieve the rewriting of the URL with the ID to the complete string URL?