I need to make web application that is acutely a desktop application The business logic will be written (taken from web app) in PHP and the underlain infra is in C++
You can use Apache as embedded web-server.
You could try PHP-GTK instead. You can do all the business logic and the presentation in PHP.
You can even try Glassfish with Qercus for PHP integration.
You could run Paste Deploy as a WSGI container for WPHP.