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We consider a Bose-Einstein condensate in a double-ring trap under rotation.We find that all ground-state configurations are stable in contrary to the findings of Ref.[1].However, the phase diagram of the system shows a surprisingly complex structure with localized defects appearing in ground state configurations.The defects have the properties of topological solitons and can be seen as BEC analogs of Josephson Vortices.We study the dynamics of the defects under the influence of external fields.