Abstract
A new finite-dimensional classical integrable system and a new quantum integrable system are generated from a spectral problem for the MKdV hierarchy through the nonlinearization technique of Lax systems. Our classical integrable 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 direct link between r -matrix formulas for classical systems and quantum problems, a quantum integrable system with separated variables is presented.
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