Classical r-matrix, new integrable system and finite boundary condition

We have analysed the classical r-matrix structure of a new integrable model in two-dimensional coupled Liouville-Thirring model. Due to the non-ultralocal character of the system, a new form of (r, -s) structure is obtained. It is also proved that the integrability of the model is not destroyed if non-trivial finite boundary conditions are imposed. An equation determining the form of the matrices K+ and K- is deduced which is a simple generalization of that of Sklyanin for the ultralocal case. (author)