Solitons Nonlinear Evolution Equations And Inverse Scattering
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Mark J. Ablowitz,Ablowitz M a,P. A. Clark,Clarkson P a
Author : Mark J. Ablowitz,Ablowitz M a,P. A. Clark,Clarkson P a Publisher : Unknown Page : 529 pages File Size : 45,5 Mb Release : 1991 Category : MATHEMATICS ISBN : 1107361613
Solitons and the Inverse Scattering Transform by Mark J. Ablowitz,Harvey Segur Pdf
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.
Topics In Soliton Theory And Exactly Solvable Nonlinear Equations: Proceedings Of The Conference On Nonlinear Evolution Equations, Solitons And The Inverse Scattering Transform by Mark J Ablowitz,Benno Fuchssteiner,M Kruskal Pdf
The focus of this volume is to show how the various successful models of nuclear structure complement one another and can be realised as approximations, appropriate in different situations, to an underlying non-relativistic many-nucleon theory of nuclei.In common with the previous volume on Foundational Models, it starts with a broad survey of the relevant nuclear structure data and proceeds with two dominant themes. The first is to review the many-body theories and successful phenomenological models with collective and nucleon degrees of freedom. The second is to show how these models relate to the underlying many-nucleon shell model in its various coupling schemes.
Loop-like Solitons in the Theory of Nonlinear Evolution Equations by V. O. Vakhnenko,E. John Parkes Pdf
This book shows that the physical phenomena and processes that take place in nature generally have complicated nonlinear features, which leads to nonlinear mathematical models for the real processes. It focuses on the practical issues involved here, as well as the development of methods to investigate the associated nonlinear mathematical problems, including nonlinear wave propagation. It acquaints the reader with a series of methods and approaches that can be applied to a wide class of nonlinear equations. The book also outlines a way in which an uninitiated reader could investigate a new nonlinear equation.
Solitons in Physics, Mathematics, and Nonlinear Optics by Peter J. Olver,David H. Sattinger Pdf
This IMA Volume in Mathematics and its Applications SOLITONS IN PHYSICS, MATHEMATICS, AND NONLINEAR OPTICS is based on the proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshops focussed on the main parts of the theory of solitons and on the applications of solitons in physics, biology and engineering, with a special concentration on nonlinear optics. We thank the Coordinating Committee: James Glimm, Daniel Joseph, Barbara Keyfitz, An Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for drew planning and implementing the stimulating year-long program. We especially thank the Workshop Organizers for Solitons in Physics and Mathematics, Alan Newell, Peter Olver, and David Sattinger, and for Nonlinear Optics and Plasma Physics, David Kaup and Yuji Kodama for their efforts in bringing together many of the major figures in those research fields in which solitons in physics, mathematics, and nonlinear optics theories are used. A vner Friedman Willard Miller, Jr. PREFACE This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 LM. A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry.
Nonlinear Evolution Equations Solvable by the Spectral Transform by F. Calogero,Francesco Calogero Pdf
The volume contains the text of the invited lectures presented at the International Symposium on "Nonlinear Evolution Equations Solvable by the Inverse Spectral Transform", that took place at the Accademia dei Lincei in Rome from June 15 through June 18, 1977. It introduces an important mathematical technique based on the spectral transform and relevant to the solution of nonlinear evolution equations. These texts will be of particular value to theoretical physicists (in plasma, nonlinear optics, hydrodynamics, solid state and elementary particles); applied mathematicians interested in nonlinear evolution equations; and pure mathematicians interested in algebraic and differential geometry.
Solitons by Boling Guo,Xiao-Feng Pang,Yu-Feng Wang,Nan Liu Pdf
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
Nonlinear Evolution Equations and Soliton Solutions by Yucui Guo Pdf
This book studies the methods for solving non-linear, partial differential equations that have physical meaning, and soliton theory with applications. Specific descriptions on the formation mechanism of soliton solutions of non-linear, partial differential equations are given, and some methods for solving this kind of solution such as the Inverse Scattering Transform method, Backlund Transformation method, Similarity Reduction method and several kinds of function transformation methods are introduced. Integrability of non-linear, partial differential equations is also discussed. This book is suitable for graduate students whose research fields are in applied mathematics, applied physics and non-linear science-related directions as a textbook or a research reference book. This book is also useful for non-linear science researchers and teachers as a reference book. The characteristics of this book are: 1. The author provides clear concepts, rigorous derivation, thorough reasoning, and rigorous logic in the book. Since the research boom of non-linear, partial differential equations was rising in the 1960s, the research on non-linear, partial differential equations and soliton theory has only been several decades, which can be described as a very young discipline compared to the other branches in mathematics. Although there are a few related books, they are mostly in highly specialised interdisciplinary areas. There is no book which is suitable for cross-disciplines and for people with college level mathematics and college physics background. This book fills that gap; 2. The book is easy to be understood by readers since it provides step-by-step approaches. All results in the book have been deduced and collated by the author to make sure that they are correct and perfect; 3. The derivation from the physical models to mathematical models is emphasised in the book. In mathematical physics, we cannot just simply consider the mathematical problems without a physical image, which often plays the key role for understanding the mathematical problems; 4. Mathematical transformation methods are provided. The basic idea of various methods for solving non-linear, partial differential equations is to simplify the complex equations into simple ones through some transformations or decompositions. However, we cannot find any patterns for using such transformations or decompositions, and certain conjectures and assumptions have to be used. However, the skill and the logic of using the transformations and decompositions are very important to researchers in this field.
