New classical and quantum integrable systems related to the MKdV integrable hierarchy

A nem finite-dimensional classical integrable system and a new quantum inte grable system are generated from a spectral problem for the MKdV hierarchy through the nonlinearization technique of Lau systems. Our classical integr able system is an example of Gaudin magnet with boundary and relates to the finite band solutions of the MKdV hierarchy. Its Lax representation and r- matrix is given, and its separation of variables is performed. Based on a d irect link between r-matrix formulas for classical systems and quantum prob lems, a quantum integrable system with separated variables is presented.