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Determinants and Their Applications in Mathematical Physics
Determinants and Their Applications in Mathematical Physics

Determinants and Their Applications in Mathematical Physics
Robert Vein, Paul Dale,
1998 | pages: 392 | ISBN: 0387985581 | PDF | 10,7 mb

This book is unique. It contains a detailed account of all important relations in the analytic theory of determinants from the classical work of Laplace, Cauchy and Jacobi in the 18th and 19th centuries to the most recent 20th century developments. Several contributions have never been published before. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. The whole of Chapter 4 is devoted to particular determinants including alternants, Wronskians and Hankelians. The contents of Chapter 5 include the Cusick and Matsuno identities. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. They include the KdV, Toda and Einstein equations. The solutions are verified by applying theorems established in earlier chapters and in the extensive appendix. The book ends with an extensive bibliography and an index. Mathematicians, physicists and engineers who wish to become acquainted with modern developments in the analytic theory of determinants will find the book indispensable.

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Hamiltonian Methods in the Theory of Solitons
Hamiltonian Methods in the Theory of Solitons

Hamiltonian Methods in the Theory of Solitons
Ludvig D. Faddeev, Leon Takhtajan, A.G. Reyman,
English | ISBN: 3540698434 | 2007 | PDF | 592 pages | 17 MB

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 Schrödinger 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 sine-Gordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions.

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... Schrödinger equation, rather than the (more usual) KdV equation, is considered as a main example. The ...
Highest Weight Representations Of Infinite Dimensional Lie Algebra
Highest Weight Representations Of Infinite Dimensional Lie Algebra

Highest Weight Representations Of Infinite Dimensional Lie Algebra
V. G. Kac, A. K. Raina,
1988 | pages: 156 | ISBN: 9971503964, 9971503956 | PDF | 3,2 mb

This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec &x27;85 and Jan &x27;86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnationsThe first is the canonical commutation relations of the infinite-dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl? of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These algebras appear in the lectures twice, in the reduction theory of soliton equations (Kp ? KdV) and in the Sugawara construction as the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. . This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite-dimensional Lie algebras; and to physicists, this theory is turning into an important component of such domains of theoretical physics as soliton theory, theory of two-dimensional statistical models, and string theory.

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... , in the reduction theory of soliton equations (Kp ? KdV) and in the Sugawara construction as the main ...
Applications of Lie Groups to Difference Equations
Applications of Lie Groups to Difference Equations

Vladimir Dorodnitsyn, "Applications of Lie Groups to Difference Equations"
English | ISBN: 1420083090 | 2010 | 344 pages | PDF | 2,1 MB


Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods and results in a new area of application of Lie groups to difference equations, difference meshes (lattices), and difference functionals, this book focuses on the preservation of complete symmetry of original differential equations in numerical schemes. This symmetry preservation results in symmetry reduction of the difference model along with that of the original partial differential equations and in order reduction for ordinary difference equations.

A substantial part of the book is concerned with conservation laws and first integrals for difference models. The variational approach and Noether type theorems for difference equations are presented in the framework of the Lagrangian and Hamiltonian formalism for difference equations.
... for well-known equations including Burgers equation, the KdV equation, and the Schrodinger equation.Downloadhttp://extabit.com ...

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