Zeros of Polynomials and Solvable Nonlinear Evolution Equations
Zeros of Polynomials and Solvable Nonlinear Evolution Equations

Author: Francesco Calogero

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 179

ISBN-13: 1108573363

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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.

Zeros of Polynomials and Solvable Nonlinear Evolution Equations
Zeros of Polynomials and Solvable Nonlinear Evolution Equations

Author: Francesco Calogero

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 179

ISBN-13: 1108428592

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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.

Nonlinear Evolution Equations Solvable by the Spectral Transform
Nonlinear Evolution Equations Solvable by the Spectral Transform

Author: F. Calogero

Publisher: Pitman Publishing

Published: 1978

Total Pages: 292

ISBN-13:

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The volume contains the text of the invited lectures presented at the International Symposium on "Nonlinear Evolution Equations Solvable by the Inverse Spectral Transform", that took place at the Accademia dei Lincei in Rome from June 15 through June 18, 1977. It introduces an important mathematical technique based on the spectral transform and relevant to the solution of nonlinear evolution equations. These texts will be of particular value to theoretical physicists (in plasma, nonlinear optics, hydrodynamics, solid state and elementary particles); applied mathematicians interested in nonlinear evolution equations; and pure mathematicians interested in algebraic and differential geometry.

Integrable Systems and Algebraic Geometry
Integrable Systems and Algebraic Geometry

Author: Ron Donagi

Publisher: Cambridge University Press

Published: 2020-04-02

Total Pages: 421

ISBN-13: 1108715745

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A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Integrable Systems and Algebraic Geometry: Volume 1
Integrable Systems and Algebraic Geometry: Volume 1

Author: Ron Donagi

Publisher: Cambridge University Press

Published: 2020-04-02

Total Pages: 421

ISBN-13: 110880358X

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Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.

Nonlinear Systems and Their Remarkable Mathematical Structures
Nonlinear Systems and Their Remarkable Mathematical Structures

Author: Norbert Euler

Publisher: CRC Press

Published: 2019-12-06

Total Pages: 541

ISBN-13: 0429554303

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Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics

Lectures on Nonlinear Evolution Equations
Lectures on Nonlinear Evolution Equations

Author: Reinhard Racke

Publisher: Birkhäuser

Published: 2015-08-31

Total Pages: 315

ISBN-13: 3319218735

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This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.

Nonlinear Evolution Equations
Nonlinear Evolution Equations

Author: Michael G. Crandall

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 266

ISBN-13: 1483269280

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Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm's method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter's product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.