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Analytic-Bilinear Approach to Integrable Hierarchies, L.V. Bogdanov


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Автор: L.V. Bogdanov
Название:  Analytic-Bilinear Approach to Integrable Hierarchies
ISBN: 9789401059220
Издательство: Springer
Классификация: ISBN-10: 9401059225
Обложка/Формат: Paperback
Страницы: 267
Вес: 0.40 кг.
Дата издания: 10.10.2012
Серия: Mathematics and Its Applications
Язык: English
Размер: 234 x 156 x 15
Основная тема: Physics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The subject of this book is the hierarchies of integrable equations connected with the one-component and multi component loop groups. There are many publications on this subject, and it is rather well defined. Thus, the author would like t.o explain why he has taken the risk of revisiting the subject. The Sato Grassmannian approach, and other approaches standard in this context, reveal deep mathematical structures in the base of the integrable hi- erarchies. These approaches concentrate mostly on the algebraic picture, and they use a language suitable for applications to quantum field theory. Another well-known approach, the a-dressing method, developed by S. V. Manakov and V.E. Zakharov, is oriented mostly to particular systems and ex- act classes of their solutions. There is more emphasis on analytic properties, and the technique is connected with standard complex analysis. The language of the a-dressing method is suitable for applications to integrable nonlinear PDEs, integrable nonlinear discrete equations, and, as recently discovered, for t.he applications of integrable systems to continuous and discret.e geometry. The primary motivation of the author was to formalize the approach to int.e- grable hierarchies that was developed in the context of the a-dressing method, preserving the analytic struetures characteristic for this method, but omitting the peculiarit.ies of the construetive scheme. And it was desirable to find a start.-


Analytic-Bilinear Approach to Integrable Hierarchies

Автор: L.V. Bogdanov
Название: Analytic-Bilinear Approach to Integrable Hierarchies
ISBN: 0792359194 ISBN-13(EAN): 9780792359197
Издательство: Springer
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Цена: 13275.00 р.
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Описание: Presents the analytic-bilinear approach to integrable hierarchies, which gives a consistent and technically simple description of integrable hierarchies. This book shows a different way to understand rather complicated structures, using mostly standard complex analysis.

Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete

Автор: Ludwig Faddeev; Pierre Van Moerbeke; Franklin Lamb
Название: Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete
ISBN: 1402035012 ISBN-13(EAN): 9781402035012
Издательство: Springer
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Цена: 28929.00 р.
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Описание: On April 29, 1814 Napoleon landed on the island of Elba, surrounded with a personal army of 1200 men. The allies, Russia, Prussia, England and Austria, hadforcedhimintoexileafteranumberofverycostlydefeats;hewasdeprived ofallhistitles, butcouldkeepthetitleof"EmperorofElba". Historytellsusthat each morning he took long walks in the sun, reviewed his army each midday anddiscussedworldmatterswithnewlyappointedadvisors, followingthesame pattern everyday, to the great surprise of Campbell, the British of?cer who was to keep an eye on him. All this made everyone believe he was settled there for good. Napoleononcesaid: Elbaisbeautiful, butabitsmall. Elbawasde?nitely a source of inspiration; indeed, the early morning, March 6, 1815, Metternich, the chancellor of Austria was woken up by one of his aides with the stunning news that Napoleon had left Elba with his 1200 men and was marching to Paris with little resistance; A few days later he took up his throne again in the Tuileries. In spite of his insatiable hunger for battles and expansion, he is remembered as an important statesman. He was a pioneer in setting up much of the legal, administrative and political machinery in large parts of continental Europe. We gathered here in a lovely and quaint ?shing port, Marciana Marina on theislandofElba, tocelebrateoneofthepioneersofintegrablesystems, Hirota Sensei, andthisattheoccasionofhisseventiethbirthday. Trainedasaphysicist in his home university Kyushu University, Professor Hirota earned his PhD in '61 at Northwestern University with Professor Siegert in the ?eld of "Quantum Statistical mechanics". He wrote a widely appreciated Doctoral dissertation on "FunctionalIntegralrepresentationofthegrandpartitionfunction".

Integrable Hamiltonian Hierarchies

Автор: Gerdjikov Vladimir
Название: Integrable Hamiltonian Hierarchies
ISBN: 3642095771 ISBN-13(EAN): 9783642095771
Издательство: Springer
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Цена: 18284.00 р.
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Описание: This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Linear Optimal Control of Bilinear Systems

Автор: Zijad Aganovic; Zoran Gajic
Название: Linear Optimal Control of Bilinear Systems
ISBN: 3540199764 ISBN-13(EAN): 9783540199762
Издательство: Springer
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Цена: 12157.00 р.
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Описание: This book is designed to be a comprehensive treatment of linear methods to optimal control of bilinear systems. The book also examines two special classes of bilinear-quadratic control problems: namely singularly perturbed and weakly coupled bilinear control systems.

Integrable Hamiltonian Hierarchies

Автор: Vladimir Gerdjikov; Gaetano Vilasi; Alexandar Bori
Название: Integrable Hamiltonian Hierarchies
ISBN: 3540770534 ISBN-13(EAN): 9783540770534
Издательство: Springer
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Цена: 18167.00 р.
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Описание: Presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies. This work demonstrates that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform.

Integrable Hierarchies and Modern Physical Theories

Автор: Henrik Aratyn; Alexander S. Sorin
Название: Integrable Hierarchies and Modern Physical Theories
ISBN: 0792369637 ISBN-13(EAN): 9780792369639
Издательство: Springer
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Цена: 22359.00 р.
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Описание: A self-contained collection of reviews, reports and survey articles describing the background to and recent developments in integral systems and their applications in modern theoretical physics. Some articles discuss the connection of integrable models to Seiberg-Witten theory and its generalization to many gauge models possessing hidden integrability on a moduli space. New ideas are also presented on higher dimensional integrable systems and skyrmions. Other topics include two dimensional sigma and WZW models; affine and boundary integrable Toda field theories and related perturbed conformal quantum field theories; boronic and supersymmetric, discrete and differential KP and Toda-type hierarchies, their various symmetry reductions, boronic and fermionic, isospectral and non-isospectral, local and non-local flows; trigonometric Calogero-Moser systems; conjugate, orthogonal and Egorov nets.
A unique insight into integrable models that will interest serious practitioners, young researchers and graduate students starting their careers in the area.

Recursion-Theoretic Hierarchies

Автор: Hinman
Название: Recursion-Theoretic Hierarchies
ISBN: 1107168244 ISBN-13(EAN): 9781107168244
Издательство: Cambridge Academ
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Цена: 23918.00 р.
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Описание: The theory set out in this volume is the result of the meeting and common development of two currents of mathematical research: descriptive set theory and recursion theory. The author develops a general theory from which the results of both areas can be derived, making the common themes clear.

Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis

Автор: Gy?rgy Terdik
Название: Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis
ISBN: 0387988726 ISBN-13(EAN): 9780387988726
Издательство: Springer
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Цена: 14673.00 р.
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Описание: The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Ito integrals and finally chaotic Wiener-Ito spectral representation of subordinated processes.

Lectures on the Complexity of Bilinear Problems

Автор: Hans F. de Groote
Название: Lectures on the Complexity of Bilinear Problems
ISBN: 354017205X ISBN-13(EAN): 9783540172055
Издательство: Springer
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Цена: 8384.00 р.
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Bilinear Forms and Zonal Polynomials

Автор: Arak M. Mathai; Serge B. Provost; Takesi Hayakawa
Название: Bilinear Forms and Zonal Polynomials
ISBN: 0387945229 ISBN-13(EAN): 9780387945224
Издательство: Springer
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Цена: 15372.00 р.
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Описание: Deals with bilinear forms in real random vectors and their generalizations. This monograph shows how zonal polynomials may be used to analyze such forms and thus to apply these concepts in a variety of statistical settings.

Singular Bilinear Integrals

Автор: Jefferies Brian Raymond Frederick
Название: Singular Bilinear Integrals
ISBN: 9813207574 ISBN-13(EAN): 9789813207578
Издательство: World Scientific Publishing
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Цена: 12830.00 р.
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Описание: 'This is a deep and beautiful monograph in functional analysis, at the interface with mathematical physics.'Mathematical ReviewsThe integration of vector valued functions with respect to vector valued measures, especially spectral measures, is developed in view of applications in operator theory, scattering theory and semiclassical approximation in quantum physics. New techniques are developed for bilinear integration in cases where the classical approach does not apply.

An Introduction to Bispectral Analysis and Bilinear Time Series Models

Автор: T.S. Rao; M.M. Gabr
Название: An Introduction to Bispectral Analysis and Bilinear Time Series Models
ISBN: 0387960392 ISBN-13(EAN): 9780387960395
Издательство: Springer
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Цена: 16769.00 р.
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Описание: The theory of time series models has been well developed over the last thirt,y years. The most interesting feature of such a model is that its second order covariance analysis is ve~ similar to that for a linear model. This demonstrates the importance of higher order covariance analysis for nonlinear models.


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