Solitons In Multidimensions Inverse Spectral Transform Method
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Solitons In Multidimensions Inverse Spectral Transform Method
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Author : B G Konopelchenko
language : en
Publisher: World Scientific
Release Date : 1993-04-30
Solitons In Multidimensions Inverse Spectral Transform Method written by B G Konopelchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-30 with categories.
The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations.
Spectral Transform And Solitons
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Author : F. Calogero
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Spectral Transform And Solitons written by F. Calogero and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
Spectral Transform and Solitons
Solitons
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Author : Mohamed Atef Helal
language : en
Publisher: Springer Nature
Release Date : 2022-11-12
Solitons written by Mohamed Atef Helal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-12 with Science categories.
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.
The Legacy Of The Inverse Scattering Transform In Applied Mathematics
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Author : J. L. Bona
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
The Legacy Of The Inverse Scattering Transform In Applied Mathematics written by J. L. Bona and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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.
Introduction To Multidimensional Integrable Equations
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Author : B.G. Konopelchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Introduction To Multidimensional Integrable Equations written by B.G. Konopelchenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.
Kp Solitons And The Grassmannians
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Author : Yuji Kodama
language : en
Publisher: Springer
Release Date : 2017-03-24
Kp Solitons And The Grassmannians written by Yuji Kodama and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-24 with Science categories.
This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of the combinatorial aspect of the TNN Grassmannians and their parameterizations, which will be useful for solving the classification problem. This work appeals to readers interested in real algebraic geometry, combinatorics, and soliton theory of integrable systems. It can serve as a valuable reference for an expert, a textbook for a special topics graduate course, or a source for independent study projects for advanced upper-level undergraduates specializing in physics and mathematics.
Geometry And Integrability
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Author : Lionel Mason
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-20
Geometry And Integrability written by Lionel Mason and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-20 with Mathematics categories.
Most integrable systems owe their origin to problems in geometry and they are best understood in a geometrical context. This is especially true today when the heroic days of KdV-type integrability are over. Problems that can be solved using the inverse scattering transformation have reached the point of diminishing returns. Two major techniques have emerged for dealing with multi-dimensional integrable systems: twistor theory and the d-bar method, both of which form the subject of this book. It is intended to be an introduction, though by no means an elementary one, to current research on integrable systems in the framework of differential geometry and algebraic geometry. This book arose from a seminar, held at the Feza Gursey Institute, to introduce advanced graduate students to this area of research. The articles are all written by leading researchers and are designed to introduce the reader to contemporary research topics.
Integrable Hamiltonian Hierarchies
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Author : Vladimir Gerdjikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-02
Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-02 with Science categories.
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Chinese Physics Letters
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Author :
language : en
Publisher:
Release Date : 2007
Chinese Physics Letters written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Physics categories.