Quantum and classical integrable sine-Gordon model with defect

Defects which are predominant in a realistic model, usually spoil its integrability or solvability. We on the other hand show the exact integrability of a known sine-Gordon field model with a defect (DSG), at the classical as well as at the quantum level based on the Yang–Baxter equation. We find the associated classical and quantum R  -matrices and the underlying q-algebraic structures, analyzing the exact lattice regularized model. We derive algorithmically all higher conserved quantities CnCn, n=1,2,…, of this integrable DSG model, focusing explicitly on the contribution of the defect point to each CnCn. The bridging condition across the defect, defined through the Bäcklund transformation is found to induce creation or annihilation of a soliton by the defect point or its preservation with a phase shift.