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Several recently discovered properties of multiple families of specialpolynomials (some orthogonal and some not) that satisfy certain differential,difference or q-difference equations are reviewed. A general method ofconstruction of isospectral matrices defined in terms of the zeros of suchpolynomials is discussed. The method involves reduction of certain partialdifferential, differential difference and differential q-difference equationsto systems of ordinary differential equations and their subsequentlinearization about the zeros of polynomials in question. Via this process,solvable (in terms of algebraic operations) nonlinear first order systems ofordinary differential equations are constructed.

Solvable dynamical systems and isospectral matrices defined in terms of the zeros of orthogonal or otherwise special polynomials