Zeros of Polynomials and Solvable Nonlinear Evolution Equations

Francesco Calogero is Professor of Theoretical Physics (Emeritus), at the Università degli Studi di Roma 'La Sapienza', Italyof Rome, Italy. He has published numerous papers and books on physics and mathematics as well as on arms control and disarmament topics and he served as Secretary General of the Pugwash Conferences on Science and World Affairs which won the 1995 Nobel Peace Prize.

• Preface; 1. Introduction; 2. Parameter-dependent monic polynomials, definitions and key formulas; 3. A differential algorithm to compute all the zeros of a generic polynomial; 4. Solvable and integrable nonlinear dynamical systems (mainly Newtonian N-body problems in the plane); 5. Solvable systems of nonlinear partial differential equations (PDEs); 6. Generations of monic polynomials; 7. Discrete time; 8. Outlook; Appendix; References.

'This concise book discusses the mathematical tools used to model complex phenomena via systems of nonlinear equations, which can be useful to describe many-body problems. Starting from a well-established approach to solvable dynamical systems identification, the author proposes a novel algorithm that allows some of the restrictions of this approach to be eliminated and, thus, identifies more solvable/integrable N-body problems. … the book presents many examples to show its application and impact. … [It] is addressed to both applied mathematicians and theoretical physicists, and can be used as a basic text for a topical course for advanced undergraduates.' Virginia Greco, CERN Courier