So when you are on a non-existing page, you want the search button to automatically search for the title of the non-existing page, in the wiki contents ?

topbanana wrote:

Yup - that's it.

Umm, when i click on the search button, it goes to http://en.wikipedia.org/wiki/Special:Search/Sp%C3%A9cial_police like you'd want it to.

There is the header that says:

Wikipedia does not have an article with this exact name. Please search for
Spécial police in Wikipedia to check for alternative titles or spellings.

or in the default install:

You can search for this page title in other pages

And both of these pages link to the desired search.

But the search button doesn't doesn't automatically search for the missing name.

Still, the functionality is staring you in the face, I don't see a reason to have the search use the referring page by default.