Spectral Transform and Solitons PDF Download

Author: F. Calogero
Publisher: Elsevier
ISBN: 9780080875347
Category : Mathematics
Languages : en
Pages : 515

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Spectral Transform and Solitons

Author: F. Calogero
Publisher:
ISBN:
Category : Evolution equations, Nonlinear
Languages : en
Pages :

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Book Description

Author: Francesco Calogero
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: B G Konopelchenko
Publisher: World Scientific
ISBN: 9814518069
Category :
Languages : en
Pages : 304

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The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations.

Author: Mark J. Ablowitz
Publisher: SIAM
ISBN: 089871477X
Category : Mathematics
Languages : en
Pages : 433

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Book 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, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

Author: Allan P. Fordy
Publisher: Manchester University Press
ISBN: 9780719014918
Category : Evolution equations, Nonlinear
Languages : en
Pages : 472

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Book Description
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: B.G. Konopelchenko
Publisher: Springer Science & Business Media
ISBN: 1489911707
Category : Science
Languages : en
Pages : 298

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Book Description
The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.

Author: Chaohao Gu
Publisher: Springer Science & Business Media
ISBN: 3662031027
Category : Mathematics
Languages : en
Pages : 414

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Book Description
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: Ludwig Faddeev
Publisher: Springer Science & Business Media
ISBN: 3540699694
Category : Science
Languages : en
Pages : 592

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Book Description
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: Giulio Soliani
Publisher: World Scientific
ISBN: 9814513504
Category : Science
Languages : en
Pages : 837

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Book Description
This is the most up-to-date book on solitons and is divided into two parts. Part 1: Detailed introductory lectures on different aspects of solitons plus lectures on the mathematical aspects on this subject. Part 2: Is a collection of reprints on mathematical theories of solitons, solitons in field theory, solitons as particles and their properties, especially topological and physical properties. This book is aimed at a wide audience of physicists and mathematicians. It is an ideal reference book for young researchers and graduate students.