Integrability Of Nonlinear Systems

Author : Yvette Kosmann-Schwarzbach,Basil Grammaticos,K.M. Tamizhmani
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 55,6 Mb
Release : 2004-02-17
Category : Science
ISBN : 3540206302

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Integrability of Nonlinear Systems by Yvette Kosmann-Schwarzbach,Basil Grammaticos,K.M. Tamizhmani Pdf

The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Author : A.K. Prykarpatsky,Igorʹ Vladimirovich Mikiti︠u︡k
Publisher : Springer
Page : 566 pages
File Size : 53,5 Mb
Release : 1998-06-30
Category : Mathematics
ISBN : UOM:39015050785701

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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by A.K. Prykarpatsky,Igorʹ Vladimirovich Mikiti︠u︡k Pdf

Noting that their research is not yet completed, Prykarpatsky (mathematics, U. of Mining and Metallurgy, Cracow, Poland and mechanics and mathematics, NAS, Lviv, Ukraine) and Mykytiuk (mechanics and mathematics, NAS and Lviv Polytechnic State U., Ukraine) describe some of the ideas of Lie algebra that underlie many of the comprehensive integrability theories of nonlinear dynamical systems on manifolds. For each case they analyze, they separate the basic algebraic essence responsible for the complete integrability and explore how it is also in some sense characteristic for all of them. They cover systems with homogeneous configuration spaces, geometric quantization, structures on manifolds, algebraic methods of quantum statistical mechanics and their applications, and algebraic and differential geometric aspects related to infinite-dimensional functional manifolds. They have not indexed their work.

Author : Yvette Kosmann-Schwarzbach,Basil Grammaticos,K. M. Tamizhmani
Publisher : Unknown
Page : 348 pages
File Size : 49,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366214431X

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Integrability of Nonlinear Systems by Yvette Kosmann-Schwarzbach,Basil Grammaticos,K. M. Tamizhmani Pdf

Author : Alain Goriely
Publisher : World Scientific
Page : 435 pages
File Size : 42,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810235338

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Integrability and Nonintegrability of Dynamical Systems by Alain Goriely Pdf

This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space.

Author : Alain Goriely
Publisher : World Scientific
Page : 438 pages
File Size : 47,8 Mb
Release : 2001
Category : Science
ISBN : 981281194X

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Integrability and Nonintegrability of Dynamical Systems by Alain Goriely Pdf

This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space. Contents: Integrability: An Algebraic Approach; Integrability: An Analytic Approach; Polynomial and Quasi-Polynomial Vector Fields; Nonintegrability; Hamiltonian Systems; Nearly Integrable Dynamical Systems; Open Problems. Readership: Mathematical and theoretical physicists and astronomers and engineers interested in dynamical systems.

Author : Vladimir E. Zakharov
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642887031

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What Is Integrability? by Vladimir E. Zakharov Pdf

The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.

Author : Michael Tabor
Publisher : Wiley-Interscience
Page : 392 pages
File Size : 51,9 Mb
Release : 1989-01-18
Category : Mathematics
ISBN : UOM:39015015760393

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Chaos and Integrability in Nonlinear Dynamics by Michael Tabor Pdf

Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics.

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556883

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Nonlinear Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814462716

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Nonlinear Dynamical Systems of Mathematical Physics by Anonim Pdf

Author : Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani
Publisher : Unknown
Page : 460 pages
File Size : 40,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662144603

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Discrete Integrable Systems by Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani Pdf

Author : J. Hietarinta,N. Joshi,F. W. Nijhoff
Publisher : Cambridge University Press
Page : 461 pages
File Size : 47,6 Mb
Release : 2016-09
Category : Mathematics
ISBN : 9781107042728

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Discrete Systems and Integrability by J. Hietarinta,N. Joshi,F. W. Nijhoff Pdf

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Author : A.K. Prykarpatsky,I.V. Mykytiuk
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 48,8 Mb
Release : 2013-04-09
Category : Science
ISBN : 9789401149945

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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by A.K. Prykarpatsky,I.V. Mykytiuk Pdf

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).

Author : Taylor & Francis Group
Publisher : CRC Press
Page : 582 pages
File Size : 46,6 Mb
Release : 2020-12-18
Category : Electronic
ISBN : 0367732432

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Nonlinear Systems and Their Remarkable Mathematical Structures by Taylor & Francis Group Pdf

Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems

Author : Basil Nicolaenko,Darryl D. Holm,James M. Hyman
Publisher : American Mathematical Soc.
Page : 494 pages
File Size : 46,9 Mb
Release : 1986
Category : Mathematics
ISBN : 0821811258

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Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 by Basil Nicolaenko,Darryl D. Holm,James M. Hyman Pdf

Focusing on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations, this title contains papers grouped in sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems.

Author : Norbert Euler,Da-jun Zhang
Publisher : CRC Press
Page : 367 pages
File Size : 42,6 Mb
Release : 2021-09-07
Category : Mathematics
ISBN : 9781000423303

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Nonlinear Systems and Their Remarkable Mathematical Structures by Norbert Euler,Da-jun Zhang Pdf

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained