Last edited by Zololrajas

Friday, April 24, 2020 | History

1 edition of **Soliton Theory and Its Applications** found in the catalog.

- 273 Want to read
- 12 Currently reading

Published
**1995** by Springer Berlin Heidelberg in Berlin, Heidelberg .

Written in English

- Mathematics,
- Differential equations, partial,
- Numerical analysis

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, Bäcklund 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 author and his collaborators, are presented. This book has been written for specialists, as well as for teachers and students in mathematics and physics.

**Edition Notes**

Statement | edited by Chaohao Gu |

Classifications | |
---|---|

LC Classifications | QA370-380 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (xii, 403 p.) |

Number of Pages | 403 |

ID Numbers | |

Open Library | OL27088355M |

ISBN 10 | 3642081770, 3662031027 |

ISBN 10 | 9783642081774, 9783662031025 |

OCLC/WorldCa | 851387204 |

2-soliton solutions. Multi-soliton solutions can be obtained through continued application of the Bäcklund transform to the 1-soliton solution, as prescribed by a Bianchi lattice relating the transformed 2-soliton solutions of the sine-Gordon equation show some of the characteristic features of the solitons. The traveling sine-Gordon kinks and/or antikinks pass through each other.

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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 : $ Soliton Theory and Its Applications First English-Language Edition by Gu Chaohao (Editor) ISBN Format: Hardcover. Buy Soliton Theory and Its Applications on FREE SHIPPING on qualified orders.

Books Advanced Search New Releases Best Sellers & More Children's Books Textbooks Textbook Rentals Sell Us Your Books Best Books of the Month. 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. Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering by: Soliton Theory and Modern Physics / Guo Boling --Ch.

Inverse Scattering Methods / Li Yishen -- Ch. Backlund Transformations and Darboux Transformations / Gu Chaohao -- Ch. Soliton theory is an important branch of applied mathematics and mathematical physics. 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 : Chaohao Gu. This monograph provides the application of soliton theory to solve certain problems selected from the fields of mechanics. The work is based of the authors’ research, and on some specified, significant results existing in the literature.

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 : CRC Press. Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences.

Drazin and Johnson explain the generation and 5/5(1). Zabusky and M. Kruskal, Interaction of “soliton” in a collisionless plasma and recurrence of initial states, Phys. Rev. Lett. 15 (), – zbMATH CrossRef Google Scholar 3.

Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm Pure Appl. Math. 21 (), –Cited by: 1. 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. The book begins with a history of the soliton from its first sighting to the discovery of the inverse scattering method and recent ideas on the algebraic structure of soliton equations.

Chapter 2 focuses on the universal nature of these equations and how and why they arise in physical and engineering contexts as asymptotic solvability conditions.

Introduction The main characteristic of this now 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, rather than the (more usual) KdV equation, is considered as a main example. 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. In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity.

Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. Keywords: solitons, inverse scattering transform, Fourier transform, evolution equations - Hide Description A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics.

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.

This chapter discusses the theory of soliton collisions in different width-division multiplexing (WDM) channels, that is, of solitons of different frequencies. In WDM, solitons of different channels gradually overtake and pass through each other. Because the solitons interact with each other, the time of overlap is known as a collision.

Optical solitons represent one of the most exciting and fascinating concepts in modern communications, arousing special interest due to their potential applications in optical fibre communication.

This volume focuses on the explicit integration of analytical and experimental methods in nonlinear fibre optics and integrated optics. The main purpose of this book is to present the rapidly developing field of Spatial Optical Solitons starting from the basic concepts of light self-focusing and self-trapping.

It will introduce the fundamental concepts of the theory of nonlinear waves and solitons in non-integrated but physically realistic models of nonlinear optics including. This book describes both the theoretical and experimental aspects of optical soliton generation, soliton properties and the application of optical solitons to all-optical high-bit-rate communications.

Only temporal optical solitons in fibres are considered. The soliton hypothesis in neuroscience is a model that claims to explain how action potentials are initiated and conducted along axons based on a thermodynamic theory of nerve pulse propagation.

It proposes that the signals travel along the cell's membrane in the form of certain kinds of solitary sound (or density) pulses that can be modeled as model is proposed as an alternative. Theory of Probability & Its Applications. Browse TVP; FAQ; E-books. Browse e-books; Series Descriptions; Book Program; MARC Records; FAQ; Proceedings; For Authors.

Journal Author Submissions; Book Author Submissions; Subscriptions. Journal Subscription; Journal Pricing; Journal Subscription Agreement; E-book Subscription; E-book Purchase; E Author: John W. Miles. Various inversion formulae, especially the beautiful generalized Mobius inversion formula, play a central role in dealing with different enumeration problems.

We propose in this paper a new hierarchy of combinatorial numbers and a related inversion formula, and show its application in generating solutions of nonlinear partial differential Cited by: 1.

This monograph provides the application of soliton theory to solve certain problems selected from the fields of mechanics. The work is based of the authors' research, and on some specified, significant results existing in the present monograph is not a simple translation of its predecessor appeared in Publishing House of the Romanian Academy in Author: Ligia Munteanu, Stefania Donescu.

An Explicit Example: The KdV 2-Soliton Collision Let's get specific, and I think it will be easier to see what I mean. The KdV equation is a non-linear partial differential equation for a function u(x,t).If we think of the function of giving the height of the wave at time t and position x along a canal, then this equation does a pretty good job of describing what happens to the surface waves.

David Tong: TASI Lectures on Solitons These lectures were given at the Theoretical Advanced Study Institute, University of Colorado, Boulder in June They are aimed at advanced graduate students and cover solitons in gauge theories, with emphasis on applications to string theory and supersymmetric gauge dynamics.

Publisher Summary. This chapter describes quantum field theory as the fundamental theory describing particle physics. Its basic object is a field, which is a finite set of operator-valued generalized functions, that is, distributions or hyperfunctions of spacetime x ing to the statistics of particles, fields are classified into two kinds, Bosonic (commutation type) and Fermionic.

The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). Discover the world. Abstract: These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory.

The lectures consist of four sections, each dealing with a diﬀerent soliton. We start with instantons and work down in co-dimension to monopoles, vortices and, eventually, domain walls.

The book presents sound coverage of the fundamentals of lightwave technology, along with material on pulse compression techniques and rare-earth-doped fiber amplifiers and lasers. The extensively revised chapters include information on fiber-optic communication systems and the ultrafast signal processing techniques that make use of nonlinear.

The following text book entitled as 'A first course in soliton theory' by Academician Barat Nuriyev,which was published by Middle East Technical University, Department of.

Soliton theory synonyms, Soliton theory pronunciation, Soliton theory translation, English dictionary definition of Soliton theory. A pulselike wave that can exist in nonlinear systems, does not obey the superposition principle, and does not disperse.

n physics an isolated. CiteScore: ℹ CiteScore: CiteScore measures the average citations received per document published in this title. CiteScore values are based on citation counts in a given year (e.g. ) to documents published in three previous calendar years (e.g.

– 14), divided by the number of documents in these three previous years (e.g. – 14). Optical solitons theory and experiment. This book describes both the theoretical and experimental --Soliton-soliton Interactions / C.

Desem and P.L. Chu --Soliton amplification in erbium-doped fiber amplifiers and its application to soliton communication / Masataka Nakazawa --Non-linear transformation of laser radiation and. In this book leading experts describe the latest theoretical and experimental advances of linear and nonlinear parity-time (PT) symmetry in a wide range of physical subjects, with emerging applications.

A comprehensive review for newcomers to the field, or to be used as : Springer Singapore. About the book Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environments needs to be understood at upper undergraduate level, with particular.

For soliton solutions, N must be an integer and it is said to be the order or the soliton. For = an exact closed form solution also exists; it has an even more complicated form, but the same periodicity fact, all solitons with ≥ have the period = /.Their shape can easily be expressed only immediately after generation: (, =) = ()on the right there is the plot of the second order.

Davydov soliton is a quantum quasiparticle representing an excitation propagating along the protein α-helix self-trapped amide is a solution of the Davydov is named for the Soviet and Ukrainian physicist Alexander Davydov model describes the interaction of the amide I vibrations with the hydrogen bonds that stabilize the α-helix of proteins.Doctoral Program Dissipation and Dispersion in Nonlinear Differential Equations.

Mathematical Physics Seminar. Some upcoming conferences, I will attend: 8ECM Satellite Conference: Contemporary Analysis and its Applications, July 1 - 5,Portorož, Slovenia; 8ECM Minisymposium: Spectral Theory and Integrable Systems, July 5 - 11,Portorož, Slovenia.If your mathematical background is insufficient for direct entry to the MSc in Mathematics and its Applications, you may apply for this course.

the University of Kent was ranked in the top 10 for research intensity. This is a measure of the proportion of staff involved in high-quality research in the university. Soliton theory, in.