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Wednesday, April 29, 2020 | History

6 edition of Nonlinear integrable equations found in the catalog.

Nonlinear integrable equations

recursion operators, group theoretical and Hamiltonian structures of soliton equations

by Konopelchenko, B. G.

  • 29 Want to read
  • 24 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Differential equations, Nonlinear.,
  • Spectral theory (Mathematics),
  • Transformations (Mathematics),
  • Solitons.

  • Edition Notes

    Bibliography: p. [309]-361.

    Other titlesRecursion operators, group theoretical and Hamiltonian structures of soliton equations.
    StatementB.G. Konopelchenko.
    SeriesLecture notes in physics ;, 270
    Classifications
    LC ClassificationsQA372 .K79 1987
    The Physical Object
    Paginationviii, 361 p. ;
    Number of Pages361
    ID Numbers
    Open LibraryOL2376354M
    ISBN 100387175679
    LC Control Number87004671

    Algebraic Aspects of Integrable Equations Honoring the Memory of Irene Dorfman (Progress in Nonlinear Differential Equations and Their Applications Book 26) eBook: . This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincare maps, chaos, fractals and strange attractors. Nonlinear waves in integrable and nonintegrable systems. Yang, Jianke. SIAM pages $ Paperback Mathematical modeling and computation; 16 QA Yang (applied mathematics, U. of Vermont) examines nonlinear waves from integrable to non-integrable equations, from analysis to numerics, and from theory to experiment. Analysis of Di erential Equations and Integrable Systems" (Protaras, Cyprus, June 17{21, ), University of Cyprus, Nicosia, , pp. This book includes papers of participants of the Sixth International Workshop \Group Analysis of Di erential Equations and Integrable Systems". The topics.


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Nonlinear integrable equations by Konopelchenko, B. G. Download PDF EPUB FB2

Book Description. Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of.

Its comprehensive coverage of analytical and numerical methods for non-integrable systems is the first of its kind. The book also discusses in great depth a wide range of analytical methods for integrable equations and comprehensively describes efficient numerical methods for all major aspects of nonlinear wave by: Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs).

The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics Author: Pham Loi Vu.

Nonlinear Integrable Equations Recursion Operators, Group-Theoretical and Hamiltonian Structures of Soliton Equations. Authors: Konopelchenko, Boris G. Free Preview. This book is suitable for use as a supplementary text to a course in mathematical physics. A brief but self-contained exposition of the basics of Riemann surfaces and theta functions prepares the reader for the main subject of this text, namely the application of these theories to solving nonlinear integrable equations for various physical systems.

Book Title:Algebro-Geometric Approach to Nonlinear Integrable Equations (Springer Series in Nonlinear Dynamics) A brief but selfcontained exposition of the basics of Riemann surfaces and theta functions prepares the reader for the main subject of this text, namely the application of these theories to solving nonlinear integrable equations for.

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs).

The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial. Nonlinear Integrable Equations Recursion Operators, Group Theoretical and Hamiltonian Structures of Soliton Equations BC group and general integrable equations under reductions.

Pages Quadratic bundle with Z 2 grading. Towards to the general theory of recursion structure of nonlinear evolution equations.

Pages Back. It also covers in great depth analytical methods for integrable equations, and comprehensively describes efficient numerical methods for all major aspects of nonlinear wave computations. In addition, the book presents the latest experiments on nonlinear waves in optical systems and Bose- Einstein condensates, especially in periodic by: Get this from a library.

Algebro-geometric approach to nonlinear integrable equations. [E D Belokolos;] -- A brief but self-contained exposition of the basics of Riemann surfaces and theta functions prepares the reader for the main subject of this text, namely, the application of these theories to solving.

The book describes efficient numerical methods for all major aspects of nonlinear wave computations. Topics include derivation of nonlinear wave equations, integrable theory for the nonlinear Schrödinger equation, and theories for integrable equations with higher-order scattering operators.

MATLAB is used to solve numerous examples in the book. Lectures on Nonlinear Integrable Equations and their Solutions by A. Zabrodin. Publisher: Number of pages: Description: This is an introductory course on nonlinear integrable partial differential and differential-difference equations based on lectures given for students of Moscow Institute of Physics and Technology and Higher School of Economics.

This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods.

The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations.

Full Description: "Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science.

This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. Nonlinear Schr¨ odinger equations, generalized harmonic oscillators, Green’s function, prop- agator, completely integrable systems, Lax pair, Zakha rov–Shabat system.

It also covers in great depth analytical methods for integrable equations, and comprehensively describes efficient numerical methods for all major aspects of nonlinear wave computations.

In addition, the book presents the latest experiments on nonlinear waves in optical systems and Bose- Einstein condensates, especially in periodic media.

We consider an integrable model which describes light beams propagating in nonlocal nonlinear media of Cole-Cole type. The model is derived as high frequency limit of both Maxwell equations and.

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.

nonlinear integrable equations, and the KdV equation and the Toda lattice equation will be taken as two illustrative examples. The proposed idea of constructing complexitons through special determinants, for example, the Wronskian and Casorati determinants, will also work for other integrable equations.

In particular, super-complexitons can be. Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.

The book * also covers in great depth analytical methods for integrable equations. Full Description: "This book brings together several aspects of soliton theory currently available only in research papers.

Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in. N-H __ Computer Physics Communications ELSEVIER Computer Physics Communications () Algorithmic integrability tests for nonlinear differential and lattice equations 1 Willy Hereman a'2'3, al Gtaa'2'4, Michael D.

Colagrosso a,2, Antonio J. Miller 1,5 Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, COUSA h Advanced Sensors and Control Cited by: Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics.

These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics. The book provides a concise and rigor introduction to the fundamentals of methods for solving the principal problems of modern non-linear dynamics.

This monograph covers the basic issues of the theory of integrable systems and the theory of dynamical chaos both Pages: Accordingly, an integrable system is a system of differential equations whose behavior is determined by initial conditions and which can be integrated from those initial conditions.

Many systems of differential equations arising in physics are integrable. A standard example is the. nonlinear differential equations Download nonlinear differential equations or read online books in PDF, EPUB, Tuebl, and Mobi Format.

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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.

Lectures on Nonlinear Integrable Equations and their Solutions by A. Zabrodin. Publisher: Number of pages: Description: This is an introductory course on nonlinear integrable partial differential and differential-difference equations based on lectures given for students of Moscow Institute of Physics and Technology and Higher School of : Examples of such Abel-designed nonlinear integrable equations are given.

Abstract We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their Cited by: Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ∂ method.

Thus, this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton by: e W.-X.

Ma / Nonlinear Analysis 63 () e–e solutions to integrable equations can exist, and show that so-called complexiton solutions [7] are one of new exact solutions. Let us first observe an example of linear ordinary differential equations. See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations.

4 R–Z, α–ω. Bateman-Burgers equation. u t + u u x = ν u x x {\displaystyle \displaystyle u_ {t}+uu_ {x}=\nu u_ {xx}} Fluid mechanics.

Benjamin–Bona–Mahony. We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions.

These resulting wavefunctions are given in exact analytical by: This book brings together several aspects of soliton theory currently available only in research papers.

Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

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 by: 1.

Schro¨dinger equation (NLS) and nonlinear wave equation (NLW). Using these equations as examples, we illustrate the basic approaches towards defining and constructing solutions, and establishing local and global properties, though we de-fer the study of the more delicate energy-critical equations to a later chapter.

(The mass-critical. It concentrates on the Darboux matrix method for constructing explicit solutions to various integrable nonlinear PDEs. ' This book can be recommended for students and researchers who are interested in a differential-geometric approach to integrable nonlinear PDE's." (Jun.

We investigate the geometry of new classes of soliton-like weak solutions for integrable nonlinear equations. One example is the class of peakons introduced by Camassa and Holm [] for their integrable shallow water equation.

Alber, Camassa, Holm and Marsden [a] put this shallow water equation into the framework of complex integrable. Fu, Wei and Nijhoff, Frank W. Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol.Issue. p. Cited by: Book Code: MM Series: Mathematical Modeling and Computation.

Pages: Buy the Print Edition. Integrable equations are an important class of nonlinear wave equations. Notable examples include the KdV equation, the NLS equation, the sine-Gordon equation, the Kadomtsev—Petviashvili (KP) equation, and many others.

Nonlinear Waves in Integrable and Nonintegrable Systems by Jianke Yang,available at Book Depository with free delivery : Jianke Yang.Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which .ection of the author’s own research path ‘from integrable to nonintegrable equations, from analysis to numerics, and from theory to experiments’.

The physical phenomena to which this book is most relevant are nonlinear wave processes in optics and Bose-Einstein condensates.