DISCRETE AND CONTINUOUS INTEGRABLE SYSTEMS POSSESSING THE SAME NON-DYNAMICAL R-MATRIX

We consider two different Lax representations with the same Lax matrix in terms of 2 x 2 traceless matrices: one produces the discrete integ rable symplectic mapping resulting from the well-known Toda spectral p roblem under the discrete Bargmann-Gamier (BG) constraint; the other g enerates the continuous non-linearized integrable system for the c-KdV spectra problem under the corresponding BG constraint. We are surpris ed to find that the two very different (one is discrete, the other con tinuous) integrable systems possess the same non-dynamical r-matrix. ( C) 1997 Published by Elsevier Science B.V.