Solitons And Geometry
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Solitons And Geometry
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Author : S. P. Novikov
language : en
Publisher: Cambridge University Press
Release Date : 1994-09-15
Solitons And Geometry written by S. P. Novikov 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 1994-09-15 with Mathematics categories.
This is an introduction to the geometry of Hamiltonian systems from the modern point of view where the basic structure is a Poisson bracket. Using this approach a mathematical analogue of the famous 'Dirac monopole' is obtained starting from the classical top in a gravity field. This approach is especially useful in physical applications in which a field theory appears; this is the subject of the second part of the lectures, which contains a theory of conservative hydrodynamic-type systems, based on Riemannian geometry, developed over the last decade. The theory has had success in solving problems in physics, such as ones associated with dispersive analogues of shock waves, and its development has led to the introduction of new notions in geometry. The book is based on lectures given by the author in Pisa and which were intended for a non-specialist audience. It provides an introduction from which to proceed to more advanced work in the area.
Glimpses Of Soliton Theory
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Author : Alex Kasman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Glimpses Of Soliton Theory written by Alex Kasman 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 2010 with Differential equations, Partial categories.
Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --
Solitons Geometry And Topology On The Crossroad
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Author : V. M. Buchstaber
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Solitons Geometry And Topology On The Crossroad written by V. M. Buchstaber 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 1997 with Geometry categories.
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.
Solitons And Geometry
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Author : Sergeĭ Petrovich Novikov
language : en
Publisher:
Release Date : 1992
Solitons And Geometry written by Sergeĭ Petrovich Novikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
B Cklund And Darboux Transformations
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Author : C. Rogers
language : en
Publisher: Cambridge University Press
Release Date : 2002-06-24
B Cklund And Darboux Transformations written by C. Rogers 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 2002-06-24 with Mathematics categories.
This 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.
Basic Methods Of Soliton Theory
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Author : Ivan V Cherednik
language : en
Publisher: World Scientific
Release Date : 1996-08-22
Basic Methods Of Soliton Theory written by Ivan V Cherednik and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-22 with Science categories.
In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.
Solitons Geometry And Topology
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Author : V. M. Buchstaber
language : en
Publisher:
Release Date : 1997
Solitons Geometry And Topology written by V. M. Buchstaber and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
This collection contains articles reflecting the most recent activity in topology and mathematical physics presented at the S. Novikov Seminar held in Moscow. Papers in the volume are devoted to problems in geometry, topology, and mathematical physics, including applications of topology to physical problems. Such a combination is a long-standing tradition of the seminar, which originated in 1965.
Nonlinear Waves And Solitons On Contours And Closed Surfaces
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Author : Andrei Ludu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-14
Nonlinear Waves And Solitons On Contours And Closed Surfaces written by Andrei Ludu 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 2012-01-14 with Science categories.
This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering. This new edition has been thoroughly revised, expanded and updated.
B Cklund And Darboux Transformations
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Author : A. A. Coley
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
B Cklund And Darboux Transformations written by A. A. Coley 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 2001 with Mathematics categories.
This 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.