I consider a new kind of dark solitons and vortices that can exist in polariton condensates and other systems with internal resonances. The reported solutions are characterized by two very distinct localization scales, and hence are coined as dual-core dark solitons and vortices.

The analogy between the newly discovered dual-core vortices and Abrikosov vortices in superconductors of the second kind is discussed.

The results are also generalized for the dissipative systems with intrinsic bistabilities.