It is simple to compile your PHP source code into an executable. Facebook released a compiler for PHP in early-2010, called HipHop, which aims to create C++. You could then compile this code, for example using gcc, to machine-code.
The more difficult point for a complex Web-App like yours is the user interface. When compiling the way I described above, the application can be run from command line - this might work for simple tasks, but not, if your application returns HTML.
One possibility to solve this problem is PHP-GTK. PHP-GTK is a API for GTK (the graphical user interface used by Linux Ubuntu by default), written in PHP. Using this solution would have to read some documentation about this API, and you would need to rewrite some parts of your program, but it would probably be the most beautiful solution, because it would create a "native" experience.
Another possible solution could involve Adobe AIR, which lets your create programs for the desktop, using HTML, CSS and JavaScript, but I don't know if and how this would work together with your compiled PHP.
Please also note that it isn't absolutely necessary to compile your PHP for it to run on the client's computer; You could also ship the PHP-interperter right with your (uncompiled) PHP-script. Of course, compiling brings benefits, such as faster execution of the program.
-- André