Title Zeros of polynomials and solvable nonlinear evolution equations / Francesco Calogero (Sapienza University of Rome, retired)

Published Cambridge : Cambridge University Press, 2018

Click on the following:
Cambridge Core
EBSCO eBooks

Copies

Description 1 online resource Contents 880-01 Introduction -- Parameter-dependent monic polynomials : definitions and key formulas -- A differential algorithm to compute all the zeros of a generic polynomial -- Solvable and integrable nonlinear dynamical systems (mainly Newtonian N-body problems in the plane) -- Solvable systems of nonlinear partial differential equations (PDEs) -- Generations of monic polynomials -- Discrete-time -- Outlook 880-01/(S 2.4.1 The ODE γ'' = c(γ')[sup(2)]γ[sup( -1)] and Its Isochronous Variant2.4.2 The ODE γ'' = (2bar y)[sup( -1)] (γ)'[sup(2)] and Its Isochronous Variant; 2.4.3 The ODE γ = c(γ')[sup(α)] and Its Isochronous Variant; 2.4.4 The Solvable ODE γ'' = ρ(γ')[sup(2)]γ[sup( -1)]+cγ[sup(ρ)] and Related Isochronous Versions; 2.4.5 Other Solvable Cases of the ODE γ'' = c(γ')[sup(α)] γ[sup(β) and Related Isochronous Variants; 2.N Notes on Chapter 2; 3 A Differential Algorithm to Compute All the Zeros of a Generic Polynomial Summary Reporting 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 Bibliography Includes bibliographical references Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL Print version record digitized 2023. HathiTrust Digital Library committed to preserve pda MiAaHDL Subject Evolution equations -- Nonlinear Zero (The number) Polynomials. Differential equations -- Partial Differential equations -- Nonlinear SCIENCE -- Energy. SCIENCE -- Mechanics -- General. SCIENCE -- Physics -- General. Differential equations, Nonlinear Differential equations, Partial Evolution equations, Nonlinear Polynomials Zero (The number) Nullstelle Polynom Nichtlineare Evolutionsgleichung Nichtlineare partielle Differentialgleichung Form Electronic book ISBN 9781108553124 1108553125 9781108619080 1108619088

  Permalink