We explore the formation of bright dissipative solitons in cavities with built-in nonlinear resonators. The solitons in such systems are studied both analytically and numerically. We have found a different kind of bright soliton which emerges due to an intrinsic bistability of the system. The solitonic structures have discontinuity in the plasmonic part of the polaritonic field and exist due to an intrinsic multiplicity of the solution for the plasmonic resonators density. The solutions may have two profoundly different localization scales, referred to as single-and dual-core solitons. We found that the bifurcation diagrams associated with dissipative solitons reveal the existence either a single-or a dual-core soliton depending on the intensity of the fields in a cavity. It was established that the solitons of both kinds can be dynamically stable and thus can be observed experimentally. A physical system for which the predicted phenomena may occur is described in terms of the effective medium model and verified numerically.
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