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Author : Robert M. Miura
Publisher : Springer
Page : 302 pages
File Size : 52,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540382201
Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Author : Robert M. Miura
Publisher : Unknown
Page : 308 pages
File Size : 49,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662205939
Author : Robert M. Miura
Publisher : Unknown
Page : 0 pages
File Size : 45,9 Mb
Release : 1976
Category : Contact transformations
ISBN : OCLC:610006705
Author : Robert M. Miura
Publisher : Unknown
Page : 128 pages
File Size : 46,6 Mb
Release : 1974
Category : Bäcklund transformations
ISBN : OCLC:903624143
Author : Robert M. Miura
Publisher : Unknown
Page : 295 pages
File Size : 45,7 Mb
Release : 1976
Category : Electronic
ISBN : OCLC:476286595
Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 45,6 Mb
Release : 1976
Category : Contact transformations
ISBN : OCLC:954260984
Author : Mark J. Ablowitz,Harvey Segur
Publisher : SIAM
Page : 433 pages
File Size : 49,9 Mb
Release : 2006-05-15
Category : Mathematics
ISBN : 9780898714777
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.
Author : W. Eckhaus,A.M. van Harten
Publisher : Elsevier
Page : 221 pages
File Size : 42,6 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080871615
The Inverse Scattering Transformation and The Theory of Solitons
Author : Mark J. Ablowitz,P. A. Clarkson
Publisher : Cambridge University Press
Page : 532 pages
File Size : 51,5 Mb
Release : 1991-12-12
Category : Mathematics
ISBN : 9780521387309
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.
Author : Chaohao Gu
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 51,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662031025
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 : J. L. Bona,Roy Choudhury,David Kaup
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 49,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821831618
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.
Author : Pham Loi Vu
Publisher : CRC Press
Page : 453 pages
File Size : 54,6 Mb
Release : 2023-05-15
Category : Mathematics
ISBN : 9781000872057
Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time. New to the Second Edition All new chapter dealing with the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line Updated references and concluding remarks Features Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved. The ISPs are set up appropriately for constructing the Bӓckhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space. The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP.
Author : S. Novikov,S.V. Manakov,L.P. Pitaevskii,V.E. Zakharov
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 43,9 Mb
Release : 1984-05-31
Category : Mathematics
ISBN : 0306109778
Author : Muthusamy Lakshmanan
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642731938
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.
Author : Boling Guo,Xiao-Feng Pang,Yu-Feng Wang,Nan Liu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 376 pages
File Size : 50,5 Mb
Release : 2018-03-19
Category : Mathematics
ISBN : 9783110549638
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