Special polynomials associated with rational solutions of the soliton equations

Abstract:
In this talk I shall discuss special polynomials associated with rational solutions for the second Painlev\'e equation (PII) and the fourth Painlev\'e equation (PIV) and associated special polynomials associated with rational solutions of soliton equations which are solvable by the inverse scattering method, including the Korteweg-de Vries, modified Korteweg-de Vries and nonlinear Schr\"odinger equations.