Theory of Solitons PDF Download

Author: S. Novikov
Publisher: Springer Science & Business Media
ISBN: 9780306109775
Category : Mathematics
Languages : en
Pages : 298

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Author: Robert M. Miura
Publisher: Springer
ISBN: 3540382208
Category : Mathematics
Languages : en
Pages : 302

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Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974

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: W. Eckhaus
Publisher: Elsevier
ISBN: 0080871615
Category : Mathematics
Languages : en
Pages : 235

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Book Description
The Inverse Scattering Transformation and The Theory of Solitons

Author: R.K. Bullough
Publisher: Springer Science & Business Media
ISBN: 3642814484
Category : Science
Languages : en
Pages : 403

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With contributions by numerous experts

Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 0521387302
Category : Mathematics
Languages : en
Pages : 532

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Book Description
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 theory.

Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 9780521336550
Category : Mathematics
Languages : en
Pages : 244

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Book Description
This textbook is an introduction to the theory of solitons in the physical sciences.

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 : 602

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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: Boling Guo
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110549417
Category : Mathematics
Languages : en
Pages : 463

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Book Description
This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics. Contents Introduction Inverse scattering transform Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations Interaction of solitons and its asymptotic properties Hirota method Bäcklund transformations and the infinitely many conservation laws Multi-dimensional solitons and their stability Numerical computation methods for some nonlinear evolution equations The geometric theory of solitons Global existence and blow up for the nonlinear evolution equations The soliton movements of elementary particles in nonlinear quantum field The theory of soliton movement of superconductive features The soliton movements in condensed state systemsontents