An integrable chain and bi-orthogonal polynomials

An integrable chain connected to the isospectral evolution of the polynomia ls of type R - I introduced by Ismail and Masson is presented. The equation s of motion of this chain generalize the corresponding equations of the rel ativistic Toda chain introduced by Ruijsenaars. We study simple self-simila r solutions to these equations that are obtained through separation of vari ables. The corresponding polynomials are expressed in terms of the Gauss hy pergeometric function. It is shown that these polynomials are stable (up to shifts of the parameters) against Darboux transformations of the generaliz ed chain.