Apache Solr AJAX
The Apache Solr AJAX module AJAXifies Apache Solr Search Integration – if you change your query or filters, you see the new result set instantly – no need to reload the full page.
With this module, you can still bookmark your searches and click the back button to undo a query or filter change. This module respects all of Apache Solr Search Integration's settings.
Please read the documentation in the Drupal handbook: you will have to write a custom module with a single hook to finish installation of the module. If you still have issues, read the Troubleshooting section first.
The project is sponsored by Evolving Web of Montreal, Quebec, Canada.