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The mixed state of superconducting (SC) and normal (N) phases in onedimensional systems are characterized by several phase slips and localizationof the order parameter of the SC phase. The phenomenon is explained on thebasis of a complex Ginzburg Landau (CGL) model. We present a simple analysis ofthe system on multiple scales to capture localization and phase slips whenphases coexist.

Morphological changes of a superconducting phase in a mixed state with a normal current: a multiple scale analysis