Yes, there is a shortcode
The shortcode will simply show the whole ajax search results : did you mean?, header, facets, sort list, results, navigation bar.
This is the very shortcode used to show the ajax results on page /search-wpsolr/.
Paste the shortcode
in any page or post description
Add the shortcode to your theme template(s)
<?php echo do_shortcode('solr_search_shortcode'); ?>