Introduction To Soliton Theory Applications To Mechanics
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Author | : Ligia Munteanu |
Publisher | : Springer Science & Business Media |
Total Pages | : 325 |
Release | : 2006-07-06 |
Genre | : Mathematics |
ISBN | : 1402025777 |
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 | : P. G. Drazin |
Publisher | : Cambridge University Press |
Total Pages | : 244 |
Release | : 1989-02-09 |
Genre | : Mathematics |
ISBN | : 9780521336550 |
This textbook is an introduction to the theory of solitons in the physical sciences.
Author | : Ivan V Cherednik |
Publisher | : World Scientific |
Total Pages | : 264 |
Release | : 1996-08-22 |
Genre | : Science |
ISBN | : 9814499005 |
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 | : Minoru Fujimoto |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 217 |
Release | : 2014-03-01 |
Genre | : Science |
ISBN | : 1627052771 |
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
Author | : Alexandre T. Filippov |
Publisher | : Springer Science & Business Media |
Total Pages | : 282 |
Release | : 2000-09-21 |
Genre | : Mathematics |
ISBN | : 9780817636357 |
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 | : Petre P. Teodorescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 778 |
Release | : 2007-06-06 |
Genre | : Science |
ISBN | : 1402054424 |
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.
Author | : R. Grimshaw |
Publisher | : WIT Press |
Total Pages | : 209 |
Release | : 2007 |
Genre | : Science |
ISBN | : 1845641574 |
Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.
Author | : Leonid A. Dickey |
Publisher | : World Scientific |
Total Pages | : 421 |
Release | : 2003 |
Genre | : Science |
ISBN | : 9812381732 |
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics.The second edition is up-to-date and differs from the first one considerably. One third of the book (five chapters) is completely new and the rest is refreshed and edited.
Author | : Robin Stanley Johnson |
Publisher | : Cambridge University Press |
Total Pages | : 468 |
Release | : 1997-10-28 |
Genre | : Mathematics |
ISBN | : 9780521598323 |
This text considers classical and modern problems in linear and non-linear water-wave theory.
Author | : Erick J. Weinberg |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2012-08-16 |
Genre | : Science |
ISBN | : 0521114632 |
An overview of classical solutions and their consequences in quantum field theory, high energy physics and cosmology for graduates and researchers.