Resumen de Time-Dependent Polynomials with One Double Root, and Related New Solvable Systems of Nonlinear Evolution Equations

Oksana Bihun, Francesco Calogero

• Recently new solvable systems of nonlinear evolution equations—including ODEs, PDEs and systems with discrete time—have been introduced. These findings are based on certain convenient formulas expressing the kth time-derivative of a root of a time-dependent monic polynomial in terms of the kth time-derivative of the coefficients of the same polynomial and of the roots of the same polynomial as well as their time-derivatives of order less than k. These findings were restricted to the case of generic polynomials without any multiple root. In this paper some of these findings—those for k=1 and k=2—are extended to polynomials featuring one double root; and a few representative examples are reported of new solvable systems of nonlinear evolution equations.