Nonlinear Poisson Brackets

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Nonlinear Poisson Brackets

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Author : Mikhail Vladimirovich Karasev
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Nonlinear Poisson Brackets written by Mikhail Vladimirovich Karasev 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 1993 with Mathematics categories.

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

Nonlinear Poisson Brackets

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Author : Mihail Vladimirovi_ Karasev
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-06-06

Nonlinear Poisson Brackets written by Mihail Vladimirovi_ Karasev 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 2012-06-06 with Education categories.

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

Nonlinear Poisson Brackets

DOWNLOAD
Author : Mikhail Vladimirovich Karasev
language : en
Publisher:
Release Date :

Nonlinear Poisson Brackets written by Mikhail Vladimirovich Karasev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Hamiltonian systems categories.

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to descri.

Nonlinear Poisson Brackets

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Nonlinear Poisson Brackets written by 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 1989 with categories.

A hierarchy of vector fields (master symmetries) and homogeneous nonlinear Poisson structures associated with the Toda lattice are constructed and the various connections between them are investigated. Among their properties: new brackets are generated from old ones by using Lie-derivatives in the direction of certain vector fields; the infinite sequences obtained consist of compatible Poisson brackets in which the constants of motion for the Toda lattice are in involution. The vector fields in the construction are unique up to addition of a Hamiltonian vector field. Similarly the Poisson brackets are unique up to addition of a trivial Poisson bracket. These are Poisson tensors generated by wedge products of Hamiltonian vector fields. The non-trivial brackets may also be obtained by the use of r-matrices; we give formulas and prove this for the quadratic and cubic Toda brackets. We also indicate how these results can be generalized to other (semisimple) Toda flows and we give explicit formulas for the rank 2 Lie algebra of type B2. The main tool in this calculation is Dirac's constraint bracket formula. Finally we study nonlinear Poisson brackets associated with orbits through nilpotent conjugacy classes in gl(n, R) and formulate some conjectures. We determine the degree of the transverse Poisson structure through such nilpotent elements in gl(n, R) for n ≤ 7. This is accomplished also by the use of Dirac's bracket formula.

Nonlinear Dynamics Of Rotating Shallow Water Methods And Advances

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Author :
language : en
Publisher: Elsevier
Release Date : 2007-04-03

Nonlinear Dynamics Of Rotating Shallow Water Methods And Advances written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-03 with Science categories.

The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner.· Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context· Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part)· Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)

Nonlinear Poisson Brackets

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Author : Pantelis Andrea Damianou
language : en
Publisher:
Release Date :

Nonlinear Poisson Brackets written by Pantelis Andrea Damianou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Nonlinear Processes In Geophysical Fluid Dynamics

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Author : O.U. Velasco Fuentes
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27

Nonlinear Processes In Geophysical Fluid Dynamics written by O.U. Velasco Fuentes 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 2011-06-27 with Technology & Engineering categories.

A Tribute to the Scientific Work of Pedro Ripa

Nonlinear Waves Hamiltonian Systems

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Author : Ricardo Carretero-González
language : en
Publisher: Oxford University Press
Release Date : 2024-11-05

Nonlinear Waves Hamiltonian Systems written by Ricardo Carretero-González and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Mathematics categories.

Nonlinear waves are of significant scientific interest across many diverse contexts, ranging from mathematics and physics to engineering, biosciences, chemistry, and finance. The study of nonlinear waves is relevant to Bose-Einstein condensates, the interaction of electromagnetic waves with matter, optical fibers and waveguides, acoustics, water waves, atmospheric and planetary scales, and even galaxy formation. The aim of this book is to provide a self-contained introduction to the continuously developing field of nonlinear waves, that offers the background, the basic ideas, and mathematical, as well as computational methods, while also presenting an overview of associated physical applications. Originated from the authors' own research activity in the field for almost three decades and shaped over many years of teaching on relevant courses, the primary purpose of this book is to serve as a textbook. However, the selection and exposition of the material will be useful to anyone who is curious to explore the fascinating world of nonlinear waves.

Hamiltonian Mechanics Of Gauge Systems

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Author : Lev V. Prokhorov
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-22

Hamiltonian Mechanics Of Gauge Systems written by Lev V. Prokhorov 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 2011-09-22 with Science categories.

The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Fluctuational Effects In The Dynamics Of Liquid Crystals

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Author : E.I. Kats
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Fluctuational Effects In The Dynamics Of Liquid Crystals written by E.I. Kats 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 2012-12-06 with Science categories.

Liquid crystals, widely used in displays for electronic equipment and other applications, have highly unusual properties arising from the anisotropy of their molecules. It appears that some aspects of the fluid dynamics of liquid crystals, such as their viscosity, can be understood only by considering the role played by thermal fluctuations. In order to provide a theoretical framework for understanding the experimental results, the authors devote a large part of the book to a derivation of the nonlinear dynamic equations and to a discussion of linearized equations for the various types of liquid crystals. The diagrammatic and other techniques they use are of general use in condensed matter physics, and this exposition should thus be of interest to all condensed-matter theorists.