Group Theoretical Methods For Integration Of Nonlinear Dynamical Systems

Author : Andrei N. Leznov
Publisher : Birkhäuser
ISBN 13 : 3034886381
Total Pages : 308 pages
Book Rating : 4.83/5 ( download)

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Download or read book Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems written by Andrei N. Leznov and published by Birkhäuser. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.

Author : Andrei N Leznov
Publisher :
ISBN 13 : 9783034886390
Total Pages : 316 pages
Book Rating : 4.9X/5 ( download)

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Download or read book Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems written by Andrei N Leznov and published by . This book was released on 1992-04-22 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander Vitalievich Razumov
Publisher : Cambridge University Press
ISBN 13 : 0521479231
Total Pages : 271 pages
Book Rating : 4.33/5 ( download)

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Download or read book Lie Algebras, Geometry, and Toda-Type Systems written by Alexander Vitalievich Razumov and published by Cambridge University Press. This book was released on 1997-05-15 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes integrable Toda type systems and their Lie algebra and differential geometry background.

Author : Carlo Cercignani
Publisher : Birkhäuser
ISBN 13 : 3034881657
Total Pages : 391 pages
Book Rating : 4.54/5 ( download)

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Download or read book The Relativistic Boltzmann Equation: Theory and Applications written by Carlo Cercignani and published by Birkhäuser. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.

Author : Victor P. Maslov
Publisher : Birkhäuser
ISBN 13 : 3034885369
Total Pages : 305 pages
Book Rating : 4.62/5 ( download)

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Download or read book The Complex WKB Method for Nonlinear Equations I written by Victor P. Maslov and published by Birkhäuser. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Lalao Rakotomanana
Publisher : Springer Science & Business Media
ISBN 13 : 0817681329
Total Pages : 272 pages
Book Rating : 4.26/5 ( download)

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Download or read book A Geometric Approach to Thermomechanics of Dissipating Continua written by Lalao Rakotomanana and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in space. Vector algebra theory was not sufficient to compare the different velocities of a particle in the course of time. There was a need to (parallel) transport these velocities at a single point before any vector algebraic operation. The appropriate mathematical structure for this transport was the connection. I The Euclidean connection derived from the metric tensor of the referential body was the only connection used in mechanics for over two centuries. Then, major steps in the evolution of spacetime concepts were made by Einstein in 1905 (special relativity) and 1915 (general relativity) by using Riemannian connection. Slightly later, nonrelativistic spacetime which includes the main features of general relativity I It took about one and a half centuries for connection theory to be accepted as an independent theory in mathematics. Major steps for the connection concept are attributed to a series of findings: Riemann 1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918, Cartan 1923, Eshermann 1950.

Author : Bruno Cordani
Publisher : Springer Science & Business Media
ISBN 13 : 9783764369026
Total Pages : 464 pages
Book Rating : 4.27/5 ( download)

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Download or read book The Kepler Problem written by Bruno Cordani and published by Springer Science & Business Media. This book was released on 2003 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM contains Microsoft Windows program Kepler which calculates the effects of any perturbation of the Kepler problem and plots the resulting trajectories.

Author : Floyd Williams
Publisher : Springer Science & Business Media
ISBN 13 : 1461200091
Total Pages : 394 pages
Book Rating : 4.93/5 ( download)

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Download or read book Topics in Quantum Mechanics written by Floyd Williams and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

Author : Mo-lin Ge
Publisher : World Scientific
ISBN 13 : 9814602566
Total Pages : 352 pages
Book Rating : 4.63/5 ( download)

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Download or read book Quantum Groups, Integrable Statistical Models And Knot Theory - The Fifth Nankai Workshop written by Mo-lin Ge and published by World Scientific. This book was released on 1993-06-30 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures in this volume discuss topics in statistical mechanics, the geometric and algebraic approaches to q-deformation theories, two-dimensional gravity and related problems of mathematical physics, including Vassiliev invariants and the Jones polynomials, the R-matrix with Z-symmetry, reflection equations and quantum algebra, W-geometry, braid linear algebra, holomorphic q-difference systems and q-Poincaré algebra.

Author : Masaki Kashiwara
Publisher : Springer Science & Business Media
ISBN 13 : 9780817642600
Total Pages : 506 pages
Book Rating : 4.09/5 ( download)

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Download or read book MathPhys Odyssey 2001 written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2002-05-24 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.