Zeros of polynomials and solvable nonlinear evolution equations /
General Material Designation
[Book]
First Statement of Responsibility
Francesco Calogero (Sapienza University of Rome, retired).
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Cambridge :
Name of Publisher, Distributor, etc.
Cambridge University Press,
Date of Publication, Distribution, etc.
2018.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references.
CONTENTS NOTE
Text of Note
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.
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SUMMARY OR ABSTRACT
Text of Note
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.
OTHER EDITION IN ANOTHER MEDIUM
Title
Zeros of polynomials and solvable nonlinear evolution equations.