Zeros of Polynomials and Solvable Nonlinear Evolution Equations
a novel breakthrough in the identification and investigation of solvable and integrable nonlinearly coupled evolution ordinary
differential equations (ODEs) or partial differential equations (PDEs), this text includes practical examples throughout to
illustrate the theoretical concepts. Beginning with systems of ODEs, including second-order ODEs of Newtonian type, it then
discusses systems of PDEs, and systems evolving in discrete time. It reports a novel, differential algorithm which can be
used to evaluate all the zeros of a generic polynomial of arbitrary degree: a remarkable development of a fundamental mathematical
problem with a long history. The book will be of interest to applied mathematicians and mathematical physicists working in
the area of integrable and solvable non-linear evolution equations; it can also be used as supplementary reading material
for general applied mathematics or mathematical physics courses.
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;
Exploring a novel breakthrough in the identification and investigation of solvable and integrable nonlinearly
coupled evolution ordinary differential equations (ODEs) or partial differential equations (PDEs).