COUPLED INTEGRABLE SYSTEMS ASSOCIATED WITH A POLYNOMIAL SPECTRAL PROBLEM AND THEIR VIRASORO SYMMETRY ALGEBRAS

An isospectral hierarchy of commutative integrable systems associated with a polynomial spectral problem is proposed. The resulting hierarch y possesses a recursion structure controlled by a hereditary operator. The nonisospectral flows generate the time first order dependent symm etries of the isospectral hierarchy, which consitute Virasoro symmetry algebras together with commutative symmetries.