A Nonlinear Progress To Modern Soliton Theory PDF Download
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| Author | : Colin Rogers |
| Publisher | : Cambridge Scholars Publishing |
| Total Pages | : 166 |
| Release | : 2022-12-06 |
| Genre | : Mathematics |
| ISBN | : 1527591557 |
Download A Nonlinear Progress to Modern Soliton Theory Book in PDF, ePub and Kindle
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 |
| Total Pages | : 472 |
| Release | : 1990 |
| Genre | : Evolution equations, Nonlinear |
| ISBN | : 9780719014918 |
Download Soliton Theory Book in PDF, ePub and Kindle
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 |
| Total Pages | : 414 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662031027 |
Download Soliton Theory and Its Applications Book in PDF, ePub and Kindle
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 |
| Total Pages | : 264 |
| Release | : 1996-08-22 |
| Genre | : Science |
| ISBN | : 9814499005 |
Download Basic Methods Of Soliton Theory Book in PDF, ePub and Kindle
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 | : V.G. Makhankov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 453 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9400922175 |
Download Soliton Phenomenology Book in PDF, ePub and Kindle
'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 | : George L. Lamb |
| Publisher | : John Wiley & Sons |
| Total Pages | : 312 |
| Release | : 1980 |
| Genre | : Mathematics |
| ISBN | : |
Download Elements of Soliton Theory Book in PDF, ePub and Kindle
| Author | : Christos H. Skiadas |
| Publisher | : CRC Press |
| Total Pages | : 934 |
| Release | : 2017-12-19 |
| Genre | : Mathematics |
| ISBN | : 1466590440 |
Download Handbook of Applications of Chaos Theory Book in PDF, ePub and Kindle
In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
| Author | : S. Novikov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 1984-05-31 |
| Genre | : Mathematics |
| ISBN | : 9780306109775 |
Download Theory of Solitons Book in PDF, ePub and Kindle
| Author | : Ligia Munteanu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 325 |
| Release | : 2006-07-06 |
| Genre | : Mathematics |
| ISBN | : 1402025777 |
Download Introduction to Soliton Theory: Applications to Mechanics Book in PDF, ePub and Kindle
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 |
| Total Pages | : 354 |
| Release | : 1987-06-01 |
| Genre | : |
| ISBN | : 9813237953 |
Download Topics In Soliton Theory And Exactly Solvable Nonlinear Equations: Proceedings Of The Conference On Nonlinear Evolution Equations, Solitons And The Inverse Scattering Transform Book in PDF, ePub and Kindle
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.
