Smart Search is a pretty decent search solution but it's limited by what is possible with a PHP–based search engine. Most commercial search engines (e.g. DuckDuckGo, Google etc) allow you to run a custom search for your site only.

Akeeba Ticket System supports that. Just like Smart Search, you can set this up either per category or in the component's Options page.

Either in the component's Options or a ticket category's Ticket Options tab there's the InstantSearch Method drop–down. Set it to URL. This makes the Search Engine URL field show up below. You can enter the URL to your search engine there. Use the variables {site} for your site's domain name (optional) and {search} for the URL–encoded search term (mandatory). For example, to use DuckDuckGo use the URL:

https://duckduckgo.com/search.html?site={site}&q={search}

Likewise, to use Google Search use the URL:

https://google.com/search?q={search}+site%3A{site}

For Google we use a compound search query. We combine the ticket's title with the suffix site:yourdomain.com to tell the search engine to only return results from your site. This trick can work on most other search engines, e.g. for Bing:

https://bing.com/search?q={search}+site%3A{site}

You can also use the external search engine URL feature in ATS to return search results from a custom search engine you use in your Intranet / Extranet, e.g. an instance of Apache Solr, Elasticsearch etc or even a custom search component installed on your site. Anything where you can access a URL with a search query and get an HTML page back with search results can be used with Akeeba Ticket System.