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Author: F. Calogero
Publisher: Elsevier
ISBN: 0080875343
Category : Mathematics
Languages : en
Pages : 533
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Book Description
Spectral Transform and Solitons
Author: F. Calogero
Publisher: Elsevier
ISBN: 0080875343
Category : Mathematics
Languages : en
Pages : 533
Get Book Here
Book Description
Spectral Transform and Solitons
Author: Ludwig Faddeev
Publisher: Springer Science & Business Media
ISBN: 3540699694
Category : Science
Languages : en
Pages : 602
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Book Description
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Author: Allan P. Fordy
Publisher: Manchester University Press
ISBN: 9780719014918
Category : Mathematics
Languages : en
Pages : 472
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Book Description
A coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law.
Author: Mohamed Atef Helal
Publisher: Springer Nature
ISBN: 1071624571
Category : Science
Languages : en
Pages : 483
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Book Description
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
Author: R.K. Bullough
Publisher: Springer Science & Business Media
ISBN: 3642814484
Category : Science
Languages : en
Pages : 403
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Book Description
With contributions by numerous experts
Author: Christian Klein
Publisher: Springer Nature
ISBN: 3030914275
Category : Differential equations
Languages : en
Pages : 596
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Book Description
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Author: J. R. Taylor
Publisher: Cambridge University Press
ISBN: 0521405483
Category : Science
Languages : en
Pages : 474
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Book Description
Provides an overview of our current understanding of optical soliton properties introducing the subject for students and reviewing the most recent research.
Author: Piergiorgio Uslenghi
Publisher: Elsevier
ISBN: 032315039X
Category : Science
Languages : en
Pages : 437
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Book Description
Nonlinear Electromagnetics is a collection of research papers from different areas of study related to the nonlinear phenomena in electromagnetism. The book, after giving a short introduction to some mathematical techniques for nonlinear problems, covers related topics such as the history of particle physics; a physical description of the spectral transform; solitons in randomly inhomogenous media; and localized wave fields in nonlinear dispersive media. Also covered in this book are topics such as non-linear plasma-wave interaction; Lagrangian methods; electromagnetic problems in composite materials in linear and nonlinear regimes; and stationary regimes in passive nonlinear methods. The text is recommended for physicists and engineers interested in the development and applications of nonlinear electromagnetic and the mathematical expressions behind it.
Author: Dilip N. Ghosh Roy
Publisher: CRC Press
ISBN: 9780849362583
Category : Science
Languages : en
Pages : 506
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Book Description
This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.
Author: Miguel Onorato
Publisher: Springer
ISBN: 331939214X
Category : Science
Languages : en
Pages : 376
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Book Description
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.
