A Nonlinear Progress To Modern Soliton Theory

Author : Colin Rogers
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1527591557
Total Pages : 166 pages
Book Rating : 4.54/5 ( download)

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Download or read book A Nonlinear Progress to Modern Soliton Theory written by Colin Rogers and published by Cambridge Scholars Publishing. This book was released on 2022-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.

Author : Allan P. Fordy
Publisher : Manchester University Press
ISBN 13 : 9780719014918
Total Pages : 472 pages
Book Rating : 4.13/5 ( download)

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Download or read book Soliton Theory written by Allan P. Fordy and published by Manchester University Press. This book was released on 1990 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Chaohao Gu
Publisher : Springer Science & Business Media
ISBN 13 : 3662031027
Total Pages : 414 pages
Book Rating : 4.25/5 ( download)

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Download or read book Soliton Theory and Its Applications written by Chaohao Gu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ivan V Cherednik
Publisher : World Scientific
ISBN 13 : 9814499005
Total Pages : 264 pages
Book Rating : 4.02/5 ( download)

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Download or read book Basic Methods Of Soliton Theory written by Ivan V Cherednik and published by World Scientific. This book was released on 1996-08-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.

Author : Alexandre T. Filippov
Publisher : Springer Science & Business Media
ISBN 13 : 9780817636357
Total Pages : 282 pages
Book Rating : 4.58/5 ( download)

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Download or read book The Versatile Soliton written by Alexandre T. Filippov and published by Springer Science & Business Media. This book was released on 2000-09-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this engaging book, the concept of the soliton is traced from the beginning of the last century to modern times with its recent applications.

Author : Andrei Ludu
Publisher : Springer Science & Business Media
ISBN 13 : 364222895X
Total Pages : 498 pages
Book Rating : 4.57/5 ( download)

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Download or read book Nonlinear Waves and Solitons on Contours and Closed Surfaces written by Andrei Ludu and published by Springer Science & Business Media. This book was released on 2012-01-14 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering. This new edition has been thoroughly revised, expanded and updated.

Author : Muthusamy Lakshmanan
Publisher : Springer Science & Business Media
ISBN 13 : 3642731937
Total Pages : 377 pages
Book Rating : 4.38/5 ( download)

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Download or read book Solitons written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: A good deal of the material presented in this book has been prepared by top experts in the field lecturing in January 1987 at the Winter School on Solitons in Tiruchirapalli,India. The lectures begin at an elementary level but go on to include even the most recent developments in the field. The book makes a handy introduction to the various facets of the soliton concept, and will be useful both to newcomers to the field and to researchers who are interested in developments in new branches of physics and mathematics.

Author : V.G. Makhankov
Publisher : Springer Science & Business Media
ISBN 13 : 9400922175
Total Pages : 453 pages
Book Rating : 4.74/5 ( download)

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Download or read book Soliton Phenomenology written by V.G. Makhankov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ..., si j'avait Sll comment en revemr, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : Ligia Munteanu
Publisher : Springer Science & Business Media
ISBN 13 : 9781402025761
Total Pages : 338 pages
Book Rating : 4.69/5 ( download)

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Download or read book Introduction to Soliton Theory: Applications to Mechanics written by Ligia Munteanu and published by Springer Science & Business Media. This book was released on 2004-08-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.

Author : Mark J Ablowitz
Publisher : World Scientific
ISBN 13 : 9813237953
Total Pages : 354 pages
Book Rating : 4.57/5 ( download)

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Download or read book Topics In Soliton Theory And Exactly Solvable Nonlinear Equations: Proceedings Of The Conference On Nonlinear Evolution Equations, Solitons And The Inverse Scattering Transform written by Mark J Ablowitz and published by World Scientific. This book was released on 1987-06-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this volume is to show how the various successful models of nuclear structure complement one another and can be realised as approximations, appropriate in different situations, to an underlying non-relativistic many-nucleon theory of nuclei.In common with the previous volume on Foundational Models, it starts with a broad survey of the relevant nuclear structure data and proceeds with two dominant themes. The first is to review the many-body theories and successful phenomenological models with collective and nucleon degrees of freedom. The second is to show how these models relate to the underlying many-nucleon shell model in its various coupling schemes.