Symmetry in Nonlinear Mathematical Physics - 2009

Eugene Belokolos (Institute of Magnetism, Kyiv, Ukraine)

On solutions of the Richardson equation

Study of the Gaudin quantum models is known to reduce to solution of the Richardson algebraic equations. Under assumption of narrow band, a solution of the Richardson equation is described in terms of zero distribution of Laguerre polynomials for the rational case and Jacobi polynomials the trigonometrical and hyperbolic cases. Asymptotic zero distribution is considered also and characterized by quadratic rational differentials.