Soliton Theory

Author : Chaohao Gu
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 44,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662031025

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Soliton Theory and Its Applications by Chaohao Gu Pdf

Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.

Author : Ryogo Hirota
Publisher : Cambridge University Press
Page : 220 pages
File Size : 54,8 Mb
Release : 2004-07-22
Category : Mathematics
ISBN : 0521836603

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The Direct Method in Soliton Theory by Ryogo Hirota Pdf

Account of method of solving soliton equations by the inventor of the method.

Author : Alex Kasman
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 41,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852453

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Glimpses of Soliton Theory by Alex Kasman Pdf

Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --

Author : Ligia Munteanu,Stefania Donescu
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 46,5 Mb
Release : 2006-07-06
Category : Mathematics
ISBN : 9781402025778

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Introduction to Soliton Theory: Applications to Mechanics by Ligia Munteanu,Stefania Donescu Pdf

This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors’ research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.

Author : Ivan V Cherednik
Publisher : World Scientific
Page : 264 pages
File Size : 43,9 Mb
Release : 1996-08-22
Category : Science
ISBN : 9789814499002

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Basic Methods Of Soliton Theory by Ivan V Cherednik Pdf

In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.

Author : Allan P. Fordy
Publisher : Manchester University Press
Page : 472 pages
File Size : 47,5 Mb
Release : 1990
Category : Evolution equations, Nonlinear
ISBN : 0719014913

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Soliton Theory by Allan P. Fordy Pdf

A coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law.

Author : S. Novikov,S.V. Manakov,L.P. Pitaevskii,V.E. Zakharov
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 44,8 Mb
Release : 1984-05-31
Category : Mathematics
ISBN : 0306109778

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Theory of Solitons by S. Novikov,S.V. Manakov,L.P. Pitaevskii,V.E. Zakharov Pdf

Author : Ludwig Faddeev,Leon Takhtajan
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 52,7 Mb
Release : 2007-08-10
Category : Science
ISBN : 9783540699699

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Hamiltonian Methods in the Theory of Solitons by Ludwig Faddeev,Leon Takhtajan Pdf

The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.

Author : George L. Lamb
Publisher : John Wiley & Sons
Page : 310 pages
File Size : 48,7 Mb
Release : 1980
Category : Mathematics
ISBN : MINN:31951D023172946

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Elements of Soliton Theory by George L. Lamb Pdf

Author : A.S. Fokas,V.E. Zakharov
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642580451

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Important Developments in Soliton Theory by A.S. Fokas,V.E. Zakharov Pdf

In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.

Author : R.W. Carroll
Publisher : Elsevier
Page : 427 pages
File Size : 51,6 Mb
Release : 1991-11-26
Category : Science
ISBN : 0080872786

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Topics in Soliton Theory by R.W. Carroll Pdf

When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and KP equations are treated extensively, with material on NLS and AKNS systems, and in following the tau function theme one is led to conformal field theory, strings, and other topics in physics. The extensive list of references contains about 1000 entries.

Author : Colin Rogers
Publisher : Cambridge Scholars Publishing
Page : 166 pages
File Size : 55,6 Mb
Release : 2022-12-06
Category : Mathematics
ISBN : 9781527591554

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A Nonlinear Progress to Modern Soliton Theory by Colin Rogers Pdf

This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.

Author : Mark J Ablowitz,Benno Fuchssteiner,M Kruskal
Publisher : World Scientific
Page : 354 pages
File Size : 55,8 Mb
Release : 1987-06-01
Category : Electronic
ISBN : 9789813237957

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Topics In Soliton Theory And Exactly Solvable Nonlinear Equations: Proceedings Of The Conference On Nonlinear Evolution Equations, Solitons And The Inverse Scattering Transform by Mark J Ablowitz,Benno Fuchssteiner,M Kruskal Pdf

The focus of this volume is to show how the various successful models of nuclear structure complement one another and can be realised as approximations, appropriate in different situations, to an underlying non-relativistic many-nucleon theory of nuclei.In common with the previous volume on Foundational Models, it starts with a broad survey of the relevant nuclear structure data and proceeds with two dominant themes. The first is to review the many-body theories and successful phenomenological models with collective and nucleon degrees of freedom. The second is to show how these models relate to the underlying many-nucleon shell model in its various coupling schemes.

Author : David S. Ricketts,Donhee Ham
Publisher : CRC Press
Page : 191 pages
File Size : 41,9 Mb
Release : 2018-09-03
Category : Technology & Engineering
ISBN : 9781351833691

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Electrical Solitons by David S. Ricketts,Donhee Ham Pdf

The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain. Drawing on the award winning research of Carnegie Mellon’s David S. Ricketts, Electrical Solitons Theory, Design, and Applications is the first text to focus specifically on KdV solitons in the nonlinear transmission line. Divided into three parts, the book begins with the foundational theory for KdV solitons, presents the core underlying mathematics of solitons, and describes the solution to the KdV equation and the basic properties of that solution, including collision behaviors and amplitude-dependent velocity. It also examines the conservation laws of the KdV for loss-less and lossy systems. The second part describes the KdV soliton in the context of the NLTL. It derives the lattice equation for solitons on the NLTL and shows the connection with the KdV equation as well as the governing equations for a lossy NLTL. Detailing the transformation between KdV theory and what we measure on the oscilloscope, the book demonstrates many of the key properties of solitons, including the inverse scattering method and soliton damping. The final part highlights practical applications such as sharp pulse formation and edge sharpening for high speed metrology as well as high frequency generation via NLTL harmonics. It describes challenges to realizing a robust soliton oscillator and the stability mechanisms necessary, and introduces three prototypes of the circular soliton oscillator using discrete and integrated platforms.

Author : Yisong Yang
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 40,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475765489

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Solitons in Field Theory and Nonlinear Analysis by Yisong Yang Pdf

There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.