<p>I want to send an array constructed in javascript with the selected values of a multiple select. Is there a way to send this array to a php script using ajax?</p>

You can post back to your server with XML or JSON. Your javascript will have to construct the post, which in the case of XML would require you to create it in javascript.  JSON is not only lighterweight but easier to make in javascript.  Check out
JSON-PHP
for parsing JSON.
You might want to take a look at
Creating JSON Data in PHP