The Complex Wkb Method For Nonlinear Equations I
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The Complex Wkb Method For Nonlinear Equations I
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Author : Victor P. Maslov
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-08-01
The Complex Wkb Method For Nonlinear Equations I written by Victor P. Maslov 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 1994-08-01 with Science categories.
This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter- nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.
The Complex Wkb Method For Nonlinear Equations I
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Author : Victor P. Maslov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Complex Wkb Method For Nonlinear Equations I written by Victor P. Maslov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. Its central mathematical idea is to use topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrödinger equation, and also to take into account the so-called tunnel effects. Finite-dimensional linear theory is reviewed in detail. Infinite-dimensional linear theory and its applications to quantum statistics and quantum field theory, as well as the nonlinear theory (involving instantons), will be considered in a second volume.
The Complex Wkb Method For Nonlinear Equations
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Author : Viktor P. Maslov
language : en
Publisher:
Release Date : 1994
The Complex Wkb Method For Nonlinear Equations written by Viktor P. Maslov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
The Complex Wkb Method For Nonlinear Equations I
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Author : V. P. Maslov
language : en
Publisher: Birkhauser
Release Date : 1994
The Complex Wkb Method For Nonlinear Equations I written by V. P. Maslov and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
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
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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.
New Progress On Graphene Research
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Author : Jian Ru Gong
language : en
Publisher: BoD – Books on Demand
Release Date : 2013-03-27
New Progress On Graphene Research written by Jian Ru Gong and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-27 with Science categories.
This book collects some new progresses on research of graphene from theoretical and experimental aspects in a variety of topics, such as graphene nanoribbons, graphene quantum dots, and graphene-based resistive switching memory. The authors of each chapter give a unique insight about the specific intense research area of graphene. This book is suitable for graduate students and researchers with background in physics, chemistry, and materials as reference.
Borel Laplace Transform And Asymptotic Theory
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Author : Boris Yu. Sternin
language : en
Publisher: CRC Press
Release Date : 1995-10-20
Borel Laplace Transform And Asymptotic Theory written by Boris Yu. Sternin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-20 with Mathematics categories.
The resurgent function theory introduced by J. Ecalle is one of the most interesting theories in mathematical analysis. In essence, the theory provides a resummation method for divergent power series (e.g., asymptotic series), and allows this method to be applied to mathematical problems. This new book introduces the methods and ideas inherent in resurgent analysis. The discussions are clear and precise, and the authors assume no previous knowledge of the subject. With this new book, mathematicians and other scientists can acquaint themselves with an interesting and powerful branch of asymptotic theory - the resurgent functions theory - and will learn techniques for applying it to solve problems in mathematics and mathematical sciences.
Weakly Nonlocal Solitary Waves And Beyond All Orders Asymptotics
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Author : John P. Boyd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Weakly Nonlocal Solitary Waves And Beyond All Orders Asymptotics written by John P. Boyd 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 Mathematics categories.
" . . . if a physical system is capable of supporting solitary wave motions then such motions will invariably arise from quite general excitations. " - T. Maxworthy (1980), pg. 52. The discover of nonlocal solitary waves is unknown and anonymous, but he or she lived in the dry north of Australia many millenia before the birth of writing. There, on the shores of the Gulf of Carpentaria, vast cylinders of cloud roll from northeast to southwest most mornings. Perhaps 300 meters in diameter, perhaps 500 meters above the ocean, these cylinders of cloud stretch from horizon to horizon. As the cloud evaporates on the trailing edge of the wave and condenses on the leading edge, the cylinder appears to roll backwards even as it propagates inland at perhaps 10-20 meters per second. Often, a whole train of cloud-cylinders propagates from Cape Yorke Penisula across the Gulf towards the southwest across modern Burketown, perhaps as much as 500 km inland into the Northern Territory. Modern-day Australians call it the "Morning Glory". What the discover called it, so many centuries before the invention of hieroglyphics, the foundation of Ur and the coronation of the First Dynasty of China, we do not know. But unless he was very different from us, he felt awe. Physicists (Smith, 1988, and Rottman and Einaudi, 1!:!93) have identified the Morning Glory as a solitary wave.
New Trends For Hamiltonian Systems And Celestial Mechanics
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Author : Ernesto A Lacomba
language : en
Publisher: #N/A
Release Date : 1996-07-03
New Trends For Hamiltonian Systems And Celestial Mechanics written by Ernesto A Lacomba and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-03 with categories.
This volume puts together several important lectures on the Hamiltonian Systems and Celestial Mechanics to form a comprehensive and authoritative collection of works on the subject. Their relationship to several aspects of topology, mechanics and dynamical systems in general are also emphasized. The papers presented are an outgrowth of the lectures that took place during the “International Symposium on Hamiltonian Systems and Celestial Mechanics ”, which was held at Cocoyoc (Morelos, México) from September 13 to 17, 1994.