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