Ba?cklund Transformations and Their Applications
Author: Rogers
Publisher: Academic Press
Published: 1982-06-18
Total Pages: 349
ISBN-13: 008095667X
DOWNLOAD EBOOKBa?cklund Transformations and Their Applications
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Bäcklund and Darboux Transformations
Author: C. Rogers
Publisher: Cambridge University Press
Published: 2002-06-24
Total Pages: 436
ISBN-13: 9780521012881
DOWNLOAD EBOOKThis book explores the deep and fascinating connections that exist between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces as they were studied by eminent geometers of the nineteenth century. Thus, nonlinear equations governing soliton propagation and also mathematical descriptions of their remarkable interaction properties are shown to arise naturally out of the classical differential geometry of surfaces and what are termed Bäcklund-Darboux transformations.This text, the first of its kind, is written in a straightforward manner and is punctuated by exercises to test the understanding of the reader. It is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.
Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications
Author: Robert M. Miura
Publisher: Springer
Published: 2006-11-14
Total Pages: 302
ISBN-13: 3540382208
DOWNLOAD EBOOKProceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Soliton Theory and Its Applications
Author: Chaohao Gu
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 414
ISBN-13: 3662031027
DOWNLOAD EBOOKSoliton 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.
Lie-Backlund Transformations in Applications
Author: Robert L. Anderson
Publisher: SIAM
Published: 1979-06-01
Total Pages: 131
ISBN-13: 0898711517
DOWNLOAD EBOOKThis title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.
Introduction to Soliton Theory: Applications to Mechanics
Author: Ligia Munteanu
Publisher: Springer Science & Business Media
Published: 2004-08-11
Total Pages: 338
ISBN-13: 9781402025761
DOWNLOAD EBOOKThis 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.
Bäcklund and Darboux Transformations
Author: A. A. Coley
Publisher: American Mathematical Soc.
Published: 2001-01-01
Total Pages: 460
ISBN-13: 9780821870259
DOWNLOAD EBOOKThis book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.
Darboux Transformations in Integrable Systems
Author: Chaohao Gu
Publisher: Springer Science & Business Media
Published: 2006-07-09
Total Pages: 317
ISBN-13: 1402030886
DOWNLOAD EBOOKThe Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.
Perspectives of Nonlinear Dynamics: Volume 2
Author: E. Atlee Jackson
Publisher: CUP Archive
Published: 1989
Total Pages: 676
ISBN-13: 9780521426336
DOWNLOAD EBOOKThe dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.
Perspectives of Nonlinear Dynamics: Volume 1
Author: E. Atlee Jackson
Publisher: CUP Archive
Published: 1989
Total Pages: 532
ISBN-13: 9780521426329
DOWNLOAD EBOOKThe dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
