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Introduction To Soliton Theory Applications To Mechanics
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Book Synopsis Introduction to Soliton Theory: Applications to Mechanics by : Ligia Munteanu
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 2006-07-06 with total page 325 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.
Download or read book Solitons written by P. G. Drazin and published by Cambridge University Press. This book was released on 1989-02-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the theory of solitons in the physical sciences.
Book Synopsis Soliton Theory and Its Applications by : Chaohao Gu
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.
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.
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.
Book Synopsis Basic Methods Of Soliton Theory by : Ivan V Cherednik
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.
Book Synopsis Glimpses of Soliton Theory by : Alex Kasman
Download or read book Glimpses of Soliton Theory written by Alex Kasman and published by American Mathematical Soc.. This book was released on 2010 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --
Author :Alexandre T. Filippov Publisher :Springer Science & Business Media ISBN 13 :0817649743 Total Pages :261 pages Book Rating :4.8/5 (176 download)
Book Synopsis The Versatile Soliton by : Alexandre T. Filippov
Download or read book The Versatile Soliton written by Alexandre T. Filippov and published by Springer Science & Business Media. This book was released on 2010-05-18 with total page 261 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.
Book Synopsis Bäcklund and Darboux Transformations by : C. Rogers
Download or read book Bäcklund and Darboux Transformations written by C. Rogers and published by Cambridge University Press. This book was released on 2002-06-24 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the deep and fascinating connections that exist between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces as they were studied by eminent geometers of the nineteenth century. Thus, nonlinear equations governing soliton propagation and also mathematical descriptions of their remarkable interaction properties are shown to arise naturally out of the classical differential geometry of surfaces and what are termed Bäcklund-Darboux transformations.This text, the first of its kind, is written in a straightforward manner and is punctuated by exercises to test the understanding of the reader. It is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.
Book Synopsis Introduction to the Mathematical Physics of Nonlinear Waves by : Minoru Fujimoto
Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by Minoru Fujimoto and published by Morgan & Claypool Publishers. This book was released on 2014-03-01 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment
Book Synopsis Mechanical Systems, Classical Models by : Petre P. Teodorescu
Download or read book Mechanical Systems, Classical Models written by Petre P. Teodorescu and published by Springer Science & Business Media. This book was released on 2007-06-06 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the study of mechanical systems as well as its links to other sciences of nature. It presents the fundamentals behind how mechanical theories are constructed and details the solving methodology and mathematical tools used: vectors, tensors and notions of field theory. It also offers continuous and discontinuous phenomena as well as various mechanical magnitudes in a unitary form by means of the theory of distributions.
Download or read book Solitons written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Solitons written by P. G. Drazin and published by Cambridge University Press. This book was released on 1989-02-09 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Tranform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites are merely what is found in standard courses on mathematical physics and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to their solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks.
Book Synopsis Topological Solitons by : Nicholas Manton
Download or read book Topological Solitons written by Nicholas Manton and published by Cambridge University Press. This book was released on 2004-06-10 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.
Book Synopsis Hamiltonian Methods in the Theory of Solitons by : Ludwig Faddeev
Download or read book Hamiltonian Methods in the Theory of Solitons written by Ludwig Faddeev and published by Springer Science & Business Media. This book was released on 2007-08-10 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Solitons written by Muthusamy Lakshmanan and published by Springer. This book was released on 1988 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
