  The phase oscillator model with global coupling is extended to the case of
finite-range nonlocal coupling. Under suitable conditions, peculiar patterns
emerge in which a quasi-continuous array of identical oscillators separates
sharply into two domains, one composed of mutually synchronized oscillators
with unique frequency and the other composed of desynchronized oscillators with
distributed frequencies. We apply a theory similar to the one which
successfully explained the onset of collective synchronization in globally
coupled phase oscillators with frequency distribution. A space-dependent order
parameter is thus introduced, and an exact functional self-consistency equation
is derived for this quantity. Its numerical solution is confirmed to reproduce
the simulation results accurately.
