Download or read book Solitons Nonlinear Evolution Equations and Inverse Scattering written by Mark J. Ablowitz and published by Cambridge University Press. This book was released on 1991-12-12 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
Download or read book Solitons and the Inverse Scattering Transform written by Mark J. Ablowitz and published by SIAM. This book was released on 2006-05-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.
Download or read book Theory of Solitons written by S. Novikov and published by Springer Science & Business Media. This book was released on 1984-05-31 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Legacy of the Inverse Scattering Transform in Applied Mathematics written by J. L. Bona and published by American Mathematical Soc.. This book was released on 2002 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant inexperimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even morepossibilities. This volume contains new developments and state-of-the-art research arising from the conference on the ``Legacy of the Inverse Scattering Transform'' held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, ``Reviews''. This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects ofsoliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multi-soliton complexes, and on a unified approach to integrable systems via Painleve analysis. This conference provided aforum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering.
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.
Download or read book Asymptotic Analysis of Soliton Problems written by Peter Cornelis Schuur and published by Springer. This book was released on 2006-11-14 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Electrical Solitons written by David S. Ricketts and published by CRC Press. This book was released on 2018-09-03 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scattering Two Volume Set written by E. R. Pike and published by Elsevier. This book was released on 2001-10-09 with total page 1831 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering
Download or read book Solitons Instantons and Twistors written by Maciej Dunajski and published by Oxford University Press, USA. This book was released on 2010 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics.
Download or read book Conference on Inverse Scattering Theory and Application written by J. Bee Bednar and published by SIAM. This book was released on 1983-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schr dinger Equation AM 154 written by Spyridon Kamvissis and published by Princeton University Press. This book was released on 2003-08-18 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing the semiclassical behavior. In doing so they also aim to explain the observed gradient catastrophe for the underlying nonlinear elliptic partial differential equations, and to set forth a detailed, pointwise asymptotic description of the violent oscillations that emerge following the gradient catastrophe. To achieve this, the authors have extended the reach of two powerful analytical techniques that have arisen through the asymptotic analysis of integrable systems: the Lax-Levermore-Venakides variational approach to singular limits in integrable systems, and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase method for the analysis of Riemann-Hilbert problems. In particular, they introduce a systematic procedure for handling certain Riemann-Hilbert problems with poles accumulating on curves in the plane. This book, which includes an appendix on the use of the Fredholm theory for Riemann-Hilbert problems in the Hölder class, is intended for researchers and graduate students of applied mathematics and analysis, especially those with an interest in integrable systems, nonlinear waves, or complex analysis.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1987 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse and Algebraic Quantum Scattering Theory written by Barnabas Apagyi and published by Springer. This book was released on 2013-12-30 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains three interrelated, beautiful, and useful topics of quantum scattering theory: inverse scattering theory, algebraic scattering theory and supersymmetrical quantum mechanics. The contributions cover such issues as coupled-channel inversions at fixed energy, inversion of pion-nucleon scattering cross-sections into potentials, inversions in neutron and x-ray reflection, 3-dimensional fixed-energy inversion, inversion of electron scattering data affected by dipole polarization, nucleon-nucleon potentials by inversion versus meson-exchange theory, potential reversal and reflectionless impurities in periodic structures, quantum design in spectral, scattering, and decay control, solution hierarchy of Toda lattices, etc.
Download or read book Nonlinear Optical Waves written by A.I. Maimistov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.
Download or read book Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and published by Springer. This book was released on 2008-12-02 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Download or read book Solutions In Action written by Karl Lanngren and published by Elsevier. This book was released on 2012-12-02 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solitons in Action is a collection of papers that discusses the concept of a wave packer or pulse known as a soliton. One paper reviews the development of the solitary wave concept, with emphasis on the difference between a solitary wave and a soliton. The Korteweg-deVries (KdV) equation shows the interactions between infinite sets of conservation laws and the inverse scattering transform method. The Backlund transform technique produces hierarchies of multisoliton solutions for nonlinear wave equations. The Gel-'fand-Levitan algorithm can effect an inverse scattering calculation that relates changes in the scattering data to changes in the solution of corresponding wave equation. One paper points out that concepts in differential geometry can show the fundamental nature of soliton behavior and the relationship between inverse scattering and the Backlund transformation. Solitons in action can be viewed as magnetic flux propagates through a gap (between two closely-spaced superconductors) in quantum units. This view results in a simplified procedure for perturbation expansions around multisoliton solutions. This collection can prove useful for researchers involved in the study of fluid mechanics, of pure and applied sciences, of mathematical sciences, and of wave theory.
Download or read book Gravitational Solitons written by Vladimir Belinski and published by Cambridge University Press. This book was released on 2001-07-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 book explains the construction of exact soliton solutions to Einstein's theory of gravity.
