Rejman, Aleksej G.
Overview
Works:  10 works in 25 publications in 1 language and 94 library holdings 

Roles:  Translator, Author, tra 
Publication Timeline
.
Most widely held works by
Aleksej G Rejman
Hamiltonian methods in the theory of solitons by
L. D Faddeev(
Book
)
10 editions published between 1987 and 2007 in English and held by 45 WorldCat member libraries worldwide
The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation, rather than the (more usual) KdV equation, is considered as a main example. The investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sineGordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions
10 editions published between 1987 and 2007 in English and held by 45 WorldCat member libraries worldwide
The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation, rather than the (more usual) KdV equation, is considered as a main example. The investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sineGordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions
Integrable systems of classical mechanics and Lie algebras by
A. M Perelomov(
Book
)
4 editions published in 1990 in English and Undetermined and held by 20 WorldCat member libraries worldwide
4 editions published in 1990 in English and Undetermined and held by 20 WorldCat member libraries worldwide
Integrable systems of classical mechanics and Lie algebras : Volume I by
A. M Perelomov(
Book
)
2 editions published in 1990 in English and held by 18 WorldCat member libraries worldwide
This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the socalled isospectral deformation method which makes extensive use of grouptheoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Liealgebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with manybody systems of generalized CalogeroMoser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the grouptheoretic point of view. Chapter 5 investigates some additional topics related to manybody systems. The book will be valuable to students as well as researchers
2 editions published in 1990 in English and held by 18 WorldCat member libraries worldwide
This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the socalled isospectral deformation method which makes extensive use of grouptheoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Liealgebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with manybody systems of generalized CalogeroMoser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the grouptheoretic point of view. Chapter 5 investigates some additional topics related to manybody systems. The book will be valuable to students as well as researchers
Dynamical systems by
A. T Fomenko(
)
2 editions published between 1993 and 1994 in English and held by 6 WorldCat member libraries worldwide
This volume contains five surveys on dynamical systems. The first one deals with nonholonomic mechanics and gives an updated and systematic treatment ofthe geometry of distributions and of variational problems with nonintegrable constraints. The modern language of differential geometry used throughout the survey allows for a clear and unified exposition of the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc. Other surveys treat various aspects of integrable Hamiltonian systems, with an emphasis on Liealgebraic constructions. Among the topics covered are: the generalized CalogeroMoser systems based on root systems of simple Lie algebras, a ge neral rmatrix scheme for constructing integrable systems and Lax pairs, links with finitegap integration theory, topologicalaspects of integrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems (Toda lattices) using the machinery of representation theory. Readers will find all the new differential geometric and Liealgebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics
2 editions published between 1993 and 1994 in English and held by 6 WorldCat member libraries worldwide
This volume contains five surveys on dynamical systems. The first one deals with nonholonomic mechanics and gives an updated and systematic treatment ofthe geometry of distributions and of variational problems with nonintegrable constraints. The modern language of differential geometry used throughout the survey allows for a clear and unified exposition of the earlier work on nonholonomic problems. There is a detailed discussion of the dynamical properties of the nonholonomic geodesic flow and of various related concepts, such as nonholonomic exponential mapping, nonholonomic sphere, etc. Other surveys treat various aspects of integrable Hamiltonian systems, with an emphasis on Liealgebraic constructions. Among the topics covered are: the generalized CalogeroMoser systems based on root systems of simple Lie algebras, a ge neral rmatrix scheme for constructing integrable systems and Lax pairs, links with finitegap integration theory, topologicalaspects of integrable systems, integrable tops, etc. One of the surveys gives a thorough analysis of a family of quantum integrable systems (Toda lattices) using the machinery of representation theory. Readers will find all the new differential geometric and Liealgebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics
Integrable systems of classical mechanics and Lie algebras by
A. M Perelomov(
Book
)
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
New results on the Kowalewski top: a Lax pair, genaralizations and algebraicgeometric solutions by
A. G Reyman(
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
Integrable systems of classical mechanics and lie algebras by
A. M Perelomov(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
Grouptheoretical methods in the theory of finitedimensional integrable systems by
A. G Reyman(
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Audience Level
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Associated Subjects
Chaotic behavior in systems Differentiable dynamical systems Differential equations Differential equations, Partial Global analysis (Mathematics) Hamiltonian systems Hyperbolic spaces Integral equations Inverse scattering transform Lie algebras Manifolds (Mathematics) Mathematical physics Mathematics Mechanics Nonholonomic dynamical systems Physics Science Solitons