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

• Bihun, Oksana ^[1] ; Calogero, Francesco ^[2]
  1. [1] University of Colorado
  2. [2] University of Rome “La Sapienza”
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 1, 2019, págs. 153-181
• Idioma: inglés
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• Resumen

  • 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.