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| Author | : Krzysztof Marciniak |
| Publisher | : |
| Total Pages | : 140 |
| Release | : 1998 |
| Genre | : |
| ISBN | : 9789172192348 |
| Author | : Jens Hoppe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 109 |
| Release | : 1992-07-10 |
| Genre | : Mathematics |
| ISBN | : 3540557008 |
Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.
| Author | : Molin Ge |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 596 |
| Release | : 2016-02-16 |
| Genre | : Science |
| ISBN | : 9814340960 |
This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.
| Author | : Ludwig Faddeev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 602 |
| Release | : 2007-08-10 |
| Genre | : Science |
| ISBN | : 3540699694 |
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 | : Boris A Kuperschmidt |
| Publisher | : World Scientific |
| Total Pages | : 399 |
| Release | : 1990-10-25 |
| Genre | : Science |
| ISBN | : 9814506737 |
Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.
| Author | : L.A. Dickey |
| Publisher | : World Scientific |
| Total Pages | : 328 |
| Release | : 1991 |
| Genre | : Science |
| ISBN | : 9789810236847 |
The theory of soliton equations and integrable systems has developed rapidly during the last 20 years with numerous applications in mechanics and physics. For a long time books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this followed one single work by Gardner, Greene, Kruskal, and Miura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.
| Author | : Tetsuji Miwa |
| Publisher | : Cambridge University Press |
| Total Pages | : 128 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780521561617 |
The notion of solitons arose with the study of partial differential equations at the end of the 19th century. In more recent times their study has involved ideas from other areas of mathematics such as algebraic gometry, topology, and in particular infinite dimensional Lie algebras, and it this approach that is the main theme of this book.This book will be of great interest to all whose research interests involves the mathematics of solitons.
| Author | : Alan C. Newell |
| Publisher | : SIAM |
| Total Pages | : 259 |
| Release | : 1985-06-01 |
| Genre | : 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 | : Vladimir G. Ivancevic |
| Publisher | : World Scientific |
| Total Pages | : 855 |
| Release | : 2008 |
| Genre | : Science |
| ISBN | : 9812819274 |
This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body ?? all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosmology. Lastly, the book turns to the human body and mind, applying quantum theory to electro-muscular stimulation and consciousness. It can be used as a graduate (or advanced undergraduate) textbook for a two-semester course in quantum physics and its modern applications. Some parts of the book can also be used by engineers, biologists, psychologists and computer scientists, as well as applied mathematicians, both in industry and academia.
| Author | : Yvette Kosmann-Schwarzbach |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 358 |
| Release | : 2004-02-17 |
| Genre | : Science |
| ISBN | : 9783540206309 |
The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
