Author : Yisong Yang
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 11,47 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 1475765487
There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.
Author : Chaohao Gu
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 26,17 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 3662031027
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 : Nicholas Manton
Publisher : Cambridge University Press
Page : 507 pages
File Size : 20,69 MB
Release : 2004-06-10
Category : Science
ISBN : 1139454692
Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.
Author : Alan C. Newell
Publisher : SIAM
Page : 259 pages
File Size : 45,87 MB
Release : 1985-06-01
Category : Technology & Engineering
ISBN : 0898711967
A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.
Author : Mark J. Ablowitz
Publisher : Cambridge University Press
Page : 532 pages
File Size : 14,12 MB
Release : 1991-12-12
Category : Mathematics
ISBN : 0521387302
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 : P. G. Drazin
Publisher : Cambridge University Press
Page : 244 pages
File Size : 19,14 MB
Release : 1989-02-09
Category : Mathematics
ISBN : 9780521336550
This textbook is an introduction to the theory of solitons in the physical sciences.
Author : Morikazu Toda
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 23,80 MB
Release : 2012-12-06
Category : Science
ISBN : 3642832199
Soliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.
Author : Lokenath Debnath
Publisher : CUP Archive
Page : 376 pages
File Size : 31,17 MB
Release : 1983-12-30
Category : Mathematics
ISBN : 9780521254687
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Author : Antonio Ambrosetti
Publisher : Cambridge University Press
Page : 184 pages
File Size : 47,39 MB
Release : 1995-03-09
Category : Mathematics
ISBN : 9780521485739
This is an elementary and self-contained introduction to nonlinear functional analysis and its applications, especially in bifurcation theory.
Author : Yuri S. Kivshar
Publisher : Academic Press
Page : 557 pages
File Size : 15,10 MB
Release : 2003-06-12
Category : Technology & Engineering
ISBN : 0080538096
The current research into solitons and their use in fiber optic communications is very important to the future of communications. Since the advent of computer networking and high speed data transmission technology people have been striving to develop faster and more reliable communications media. Optical pulses tend to broaden over relatively short distances due to dispersion, but solitons on the other hand are not as susceptible to the effects of dispersion, and although they are subject to losses due to attenuation they can be amplified without being received and re-transmitted.This book is the first to provide a thorough overview of optical solitons. The main purpose of this book is to present the rapidly developing field of Spatial Optical Solitons starting from the basic concepts of light self-focusing and self-trapping. It will introduce the fundamental concepts of the theory of nonlinear waves and solitons in non-integrated but physically realistic models of nonlinear optics including their stability and dynamics. Also, it will summarize a number of important experimental verification of the basic theoretical predictions and concepts covering the observation of self-focusing in the earlier days of nonlinear optics and the most recent experimental results on spatial solitons, vortex solitons, and soliton interaction & spiraling.* Introduces the fundamental concepts of the theory of nonlinear waves and solitons through realistic models * Material is based on authors' years of experience actively working in and researching the field* Summarizes the most important experimental verification of the basic theories, predictions and concepts of this ever evolving field from the earliest studies to the most recent
