I see myself doing the following code for default assigment all the type on PHP
$variable = $variable ? $variable : 'default value';
$variable = $variable ?: 'default value';
$variable ?= 'default value';
You cannot create new operators in PHP without changing the PHP source.
And you don't want to change it, trust me. Sure, it'd be easy enough - PHP is open source and uses a straightforward LALR(1) parser which you could easily modify - but that would make your code incompatible with the standard PHP implementation. You would thus very much restrict who can run the code - which will probably be nobody apart from you, as nobody else will care to modify their PHP engine just to run your code.
Update: I wrote a small tutorial on how to add new syntax (like operators) to PHP: http://nikic.github.com/2012/07/27/How-to-add-new-syntactic-features-to-PHP.html