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Author: Alexandre T. Filippov
Publisher: Springer Science & Business Media
ISBN: 0817649743
Category : Mathematics
Languages : en
Pages : 275
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Book Description
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: Alexandre T. Filippov
Publisher: Springer Science & Business Media
ISBN: 0817649743
Category : Mathematics
Languages : en
Pages : 275
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Book Description
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: Sergei Eremenko
Publisher: Amazon
ISBN: 1951630777
Category : Science
Languages : en
Pages : 341
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Book Description
Dedicated to a broad audience and scientists, this new-generation, easy-to-read, pictorial, interactive book uses beautiful photography, video channel, and computer scripts in R and Python to demonstrate existing and explore new solitons – the magnificent and versatile energy concentration phenomenon of nature. With 200 images and videos collected around the world and on magnificent Australian beaches, we describe captivating stand-alone ocean solitons capable of travelling hundreds of miles uninterrupted. Along with scary tsunamis, the tricky solitonic bores propagating upstream narrow river channels may cause disasters for coastal cities. Sudden killer rogue waves endanger even large ships. Powerful tornadoes, surfing tubes, whirlpools and rotating galaxies are solitonic vortices. Unique videos of breathers and soliton envelope waves, with legendary 'Ninth Wave' in the middle, are commented by some legendary scientists. Beautiful photography of square grid waves confirms tendency of nature to produce multi-dimensional formations. Solitonic dislocations and defects are widespread in metal shapes around us. Solitonic energy localization effects appear in swing movements of humans perfected them in many sports and dances. We also explore new solitonic hypothesis and theories. Geosolitons may have played an important role in formation of mountain ranges and sedimentary rocks. Using solitonic functions for heart blood pressure pulses may lead to new-generation devices. Solitonic dislocation and stability effects may exist in behaviour of correlated financial markets. New class of atomic solitons can be used to describe Higgs boson (‘the god particle’) fields, spacetime quanta and other fundamental building blocks of nature. Readers are welcomed to subscribe and provide own videos to our dedicated video channel and website www.solitonnature.com.
Author: Alex Kasman
Publisher: American Mathematical Society
ISBN: 1470472627
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar. —William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition) Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena like rogue waves and DNA transcription. Solitons of light are even used by engineers for data transmission and optical switches. Furthermore, unlike most nonlinear partial differential equations, soliton equations have the remarkable property of being exactly solvable. Explicit solutions to those equations provide a rare window into what is possible in the realm of nonlinearity. Glimpses of Soliton Theory reveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. 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 explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra, the book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Hierarchy, and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make the subject accessible to undergraduates, numerous worked examples and thought-provoking exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of Mathematica® to facilitate computation and animate solutions. The second edition refines the exposition in every chapter, adds more homework exercises and projects, updates references, and includes new examples involving non-commutative integrable systems. Moreover, the chapter on KdV multisolitons has been greatly expanded with new theorems providing a thorough analysis of their behavior and decomposition.
Author: David S. Ricketts
Publisher: CRC Press
ISBN: 1351833693
Category : Technology & Engineering
Languages : en
Pages : 203
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Book Description
The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain. Drawing on the award winning research of Carnegie Mellon’s David S. Ricketts, Electrical Solitons Theory, Design, and Applications is the first text to focus specifically on KdV solitons in the nonlinear transmission line. Divided into three parts, the book begins with the foundational theory for KdV solitons, presents the core underlying mathematics of solitons, and describes the solution to the KdV equation and the basic properties of that solution, including collision behaviors and amplitude-dependent velocity. It also examines the conservation laws of the KdV for loss-less and lossy systems. The second part describes the KdV soliton in the context of the NLTL. It derives the lattice equation for solitons on the NLTL and shows the connection with the KdV equation as well as the governing equations for a lossy NLTL. Detailing the transformation between KdV theory and what we measure on the oscilloscope, the book demonstrates many of the key properties of solitons, including the inverse scattering method and soliton damping. The final part highlights practical applications such as sharp pulse formation and edge sharpening for high speed metrology as well as high frequency generation via NLTL harmonics. It describes challenges to realizing a robust soliton oscillator and the stability mechanisms necessary, and introduces three prototypes of the circular soliton oscillator using discrete and integrated platforms.
Author: Yakov M. Shnir
Publisher: Cambridge University Press
ISBN: 1108429912
Category : Science
Languages : en
Pages : 281
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Book Description
An introduction to integrable and non-integrable scalar field models, with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, this book brings together discussion of solitary waves and construction of soliton solutions and provides a discussion of solitons using simple model examples.
Author: A. Mourachkine
Publisher: Springer Science & Business Media
ISBN: 0306480638
Category : Science
Languages : en
Pages : 326
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Book Description
“The Frontiers of Knowhledge (to coin a phrase) are always on the move. - day’s discovery will tomorrow be part of the mental furniture of every research worker. By the end of next week it will be in every course of graduate lectures. Within the month there will be a clamour to have it in the undergraduate c- riculum. Next year, I do believe, it will seem so commonplace that it may be assumed to be known by every schoolboy. “The process of advancing the line of settlements, and cultivating and c- ilizing the new territory, takes place in stages. The original papers are p- lished, to the delight of their authors, and to the critical eyes of their readers. Review articles then provide crude sketch plans, elementary guides through the forests of the literature. Then come the monographs, exact surveys, mapping out the ground that has been won, adjusting claims for priority, putting each fact or theory into its place” (J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, 1972) p.v). The main purpose of the book is to present the mechanism of - perconductivity discovered in 1986 by J. G. Bednorz and K. A. Müller, and to discuss the physics of superconductors. The last chapter of the book presents analysis of tunneling measurements in cuprates. The book is - dressed to researchers and graduate students in all branches of exact sciences.
Author: Mohamed Atef Helal
Publisher: Springer Nature
ISBN: 1071624571
Category : Science
Languages : en
Pages : 483
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Book Description
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
Author: Michael I. Monastyrsky
Publisher: Springer Science & Business Media
ISBN: 0817647791
Category : Mathematics
Languages : en
Pages : 220
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Book Description
The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter.
Author: Bijoy Ghosh
Publisher: Springer
ISBN: 3642036279
Category : Technology & Engineering
Languages : en
Pages : 288
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Book Description
Papers in this collection partly represent the set of talks that were presented at Texas Tech University on the occasion of Daya’s memorial workshop in the year 2007. Daya had a varied interest in the field of Dynamics and Control Theory and the papers bring out the essence of his involvement in these activities. He also had a large number of collaborators and this collection represent a good fraction of them. The papers included here cover his interest in control theory. Also included are papers from application areas that we believe are of strong interest to him.
Author: A.S. Fokas
Publisher: Springer Science & Business Media
ISBN: 3642777694
Category : Science
Languages : en
Pages : 343
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Book Description
In 1979, a historical meeting took place at the Institute for Theoretical Physics in Kiev, USSR, where 48 American Scientists, specialists in nonlinear and turbulent processes, met for two weeks with their soviet counterparts. This meeting pro vided the unique opportunity for USA and USSR participants to directly interact personally and scientifically with each other. This interaction was of great impor not only for the individuals involved but also for the science of nonlinear tance phenomena in general. At the end of the meeting, it was agreed that this exchange should continue, and it was decided to have the next meeting in the USA in 1981. Unfortunately, due to the political situation at that time, the second meeting in the USA never materialized. However, in 1983, the Soviet scientists organized in Kiev a second Workshop. This second meeting was again quite successful. Similar meetings, with growing success were organized at Kiev in 1987, and 1989. It should be noted that 405 participants from 22 countries participated at the fourth Kiev workshop on Nonlinear and Turbulent Processes. The Chainnan of this workshop was V. Zakharov, who has also been a co-chainnan of all the previous workshops.
