Abstract
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.
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