Hamiltonian methods in the theory of solitons by L. D. Faddeev

Cover of: Hamiltonian methods in the theory of solitons | L. D. Faddeev

Published by Springer-Verlag in Berlin, New York .

Written in English

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Subjects:

  • Solitons.,
  • Inverse scattering transform.,
  • Hamiltonian systems.,
  • Mathematical physics.

Edition Notes

Book details

StatementL.D. Faddeev, L.A. Takhtajan ; translated from the Russian by A.G. Reyman.
SeriesSpringer series in Soviet mathematics
ContributionsTakhtadzhi͡a︡n, L. A.
Classifications
LC ClassificationsQC174.26.W28 F3313 1987
The Physical Object
Paginationix, 592 p. ;
Number of Pages592
ID Numbers
Open LibraryOL2736933M
ISBN 100387155791
LC Control Number86031410

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Hamiltonian Method in the Theory of Solitons. Hamiltonian Methods in the Theory of Solitons; This conclusion is intended for those who have read the book to the end.

We hope that the main. This book presents the foundations of the inverse scattering method and its applications to the theory of solitons in such a form as we understand it in Leningrad.

The concept of solitonwas introduced by Kruskal and Zabusky in A soliton (a solitary wave) is a localized particle-like solution. 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. Over the past fifteen years the theory of solitons and the related theory of integrable nonlinear evolution equations in two space-time dimensions has attracted a large number of research workers of different orientations ranging from algebraic geometry to applied hydrodynamics.

Modern mathematical physics has witnessed the development of a vast new area of research devoted to this theory and. Hamiltonian methods in the theory of solitons. Berlin ; New York: Springer-Verlag, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: L D Faddeev; L A Takhtadzhi︠a︡n.

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.

Rating: (not yet rated) 0 with reviews. Buy Hamiltonian Methods in the Theory of Solitons (Classics in Mathematics) on FREE SHIPPING on qualified orders Hamiltonian Methods in the Theory of Solitons (Classics in Mathematics): Faddeev, L.

D., Reyman, A. G., Takhtajan, Leon A.: : BooksCited by:   This book presents the foundations of the inverse scattering method and its applications to the theory of solitons in such a form as we understand it in Leningrad.

The concept of solitonwas introduced by Kruskal and Zabusky in A soliton (a solitary wave) is a localized particle-like solution of a nonlinear equation which describes excitations of finite energy and exhibits several. Hamiltonian Methods in the Theory of Solitons (Springer Series in Soviet Mathematics) Reprint of the 1st e Edition by L.

Faddeev (Author) › Visit Amazon's L. Faddeev Page. Find all the books, read about the author, and more. See search results for this author 5/5(1). 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 Price: $ hamiltonian methods in the theory of solitons | Get Read & Download Ebook hamiltonian methods in the theory of solitons as PDF for provide copy of haunted women of the otherworld book 5 in digital format, so the resources that you find are reliable.

There are also many Ebooks of related with this subject. Hamiltonian Methods in the Theory of Solitons Ludwig D. Faddeev, Leon A. Takhtajan (auth.) 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.

Hamiltonian Methods in the Theory of Solitons Faddeev, Ludwig D. Abstract. Publication: Hamiltonian Methods in the Theory of Solitons: Pub Date: DOI: / Bibcode: .F Keywords: Physics; full text sources.

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Hamiltonian Methods in the Theory of Solitons; Hamiltonian Methods in the Theory of Solitons; Hamiltonian Methods in the Theory of Solitons; Applied Methods of the Theory of Random Functions: International Series of Monographs in Pure and Applied Mathematics, Vol.

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Hamiltonian Methods in the Theory of Solitons 英文书摘要 The investigation of this equation forms the first part of the book.

The second part is devoted to such fundamental models as the sine-Gordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions. Find many great new & used options and get the best deals for Classics in Mathematics Ser.: Hamiltonian Methods in the Theory of Solitons by Leon A.

Takhtajan and Ludwig D. Faddeev (Perfect) at the best online prices at eBay. Free shipping for many products. In quantum mechanics, a Hamiltonian is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system (this addition is the total energy of the system in most of the cases under analysis).

It is usually denoted by, but also or ^ to highlight its function as an operator. Its spectrum is the set of possible outcomes when one measures. Hamiltonian mechanics is an equivalent but more abstract reformulation of classical mechanic ically, it contributed to the formulation of statistical mechanics and quantum mechanics.

Hamiltonian mechanics was first formulated by William Rowan Hamilton instarting from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange. "Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity.

The papers cover a wide range of topics but share common mathematical notions and investigation techniques. Hamiltonian mechanics. The only physical principles we require the reader to know are: (i) Newton’s three laws; (ii) that the kinetic energy of a particle is a half its mass times the magnitude of its velocity squared; and (iii) that work/energy is equal to the force applied times.

This book gives a self-contained exposition of the theory of gravitational solitons and provides a comprehensive review of exact soliton solutions to Einstein's equations. The text begins with a detailed discussion of the extension of the Inverse Scattering Method to the theory of gravitation, starting with pure gravity and then extending.

"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques.

An introductory note on eight concepts. The Hamiltonian is a function used to solve a problem of optimal control for a dynamical can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time horizon.

Inspired by, but distinct from, the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as. Soliton and nonlinear wave equations.

Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. Reyman Book. Nonlinear Science at the Dawn of the 21st Century. N.H. March Liquid Metals: Concepts and Theory I. Montvay and G. M¨unster Quantum Fields on a Lattice† L.

O’Raifeartaigh Group Structure of Gauge Theories† T. Ort´ın Gravity and Strings† A.M. Ozorio de Almeida Hamiltonian Systems: Chaos and Quantization† L. Parker and D.J.

Toms Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity R. Penrose and W. Rindler Spinors. Effective Hamiltonian Theory Frank Neese Methods in Molecular Energy Research Hamiltonians and Eigensystems ★ Let us assume that we have a Hamiltonian that works on a set of variables x xN.

Hamiltonian but for most intents and purposes the second order He. TOPOLOGICAL SOLITONS Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure.

Exam-ples are monopoles and Skyrmions, Ginzburg–Landau vortices and sigma-model lumps, and Yang–Mills instantons. This book is a comprehensive survey of.

precisely, the quantity H (the Hamiltonian) that arises when E is rewritten in a certain way explained in Section But before getting into a detailed discussion of the actual Hamiltonian, let’s flrst look at the relation between E and the energy of the system.

We chose the letter E in Eq. (/) because the quantity on the right. 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.

Energy-conserving Hamiltonian Boundary Value Methods for the numerical solution of the Korteweg–de Vries equation.

it is known from the theory of Fourier methods Kruskal ction of solitons in a collisionless plasma and the recurrence of initial states. The book addresses problems in quantization, restoration of translational and rotational symmetry, and the field theoretical approach to solitons which are common problems in the field of solitons.

Primarily aimed for graduate students and the novice in the field, the collected articless cover a broad spectrum of topics in formalism as well as. Direct Methods in Soliton Theories.- Trilinear Form - an Extension of Hirota's Bilinear Form.- On the Use of Bilinear Forms for the Search of Families of Integrable Nonlinear Evolution Equations.- From Periodic Processes to Solitons and Vice-Versa.- VII Inverse Methods Related to a Linearization Scheme If the address matches an existing account you will receive an email with instructions to reset your password.

This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode.

@article{osti_, title = {Solitons and nonlinear wave equations}, author = {Dodd, Roger K and Eilbeck, J Chris and Gibbon, John D and Morris, Hedley C}, abstractNote = {A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory.

Parametric curves featuring Hamiltonian versus energy are useful in the theory of solitons in conservative nonintegrable systems with local nonlinearities. These curves can be constructed in various ways.

We show here that it is possible to find the Hamiltonian~H. and energy ~Q. for solitons of. Each chapter contains mechanical and physical examples, and the combination of advanced material and more tutorial elements makes this book attractive for both experts and non-specialists keen to expand their knowledge on modern methods and trends in stability theory.

Contents. 1.Hamiltonian mechanics, which are the subjects of later chapters. Finally, we explain why in this book, we take a mathematical perspective on central topics of classical physics. Classical physics refers to the collection of physical theories that do not use quantum theory and often predate modern quantum physics.

They can be traced back to Newton.Of course, the effective Hamiltonian is typically only calculated perturbatively to some order, so approximations are introduced. But imagine if we could find the effective Hamiltonian to all orders, then it would agree with the full Hamiltonian on any physical measurements that take place in .

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