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In this paper we discuss the Lax formulation of the Grassmanian and BosonicThirring models in the presence of jump defects. For the Grassmanian case, thedefect is described by B\"acklund transformation which is responsible forpreserving the integrability of the model.  We then propose an extension of the B\"acklund transformation for the BosonicThirring model which is verified by some B\"acklund transitions like  Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons andTwo solitons - Two solitons. The Lax formulation within the space split by thedefect leads to the integrability of Bosonic Thirring model.

Grassmanian and Bosonic Thirring Models with Jump Defects