Geometric Aspects of the Einstein Equations and Integrable Systems, Rodolfo Martini

Автор: Yuri Fedorov; Valerij Vasilievich Kozlov
Название: A Memoir on Integrable Systems
ISBN: 3540590005 ISBN-13(EAN): 9783540590002
Издательство: Springer
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Описание: This book considers the larger class of systems which are not (at least a priori) Hamiltonian but possess tensor invariants, in particular, an invariant measure.

Автор: G.F. Helminck
Название: Geometric and Quantum Aspects of Integrable Systems
ISBN: 3662139308 ISBN-13(EAN): 9783662139301
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Описание: The survey articles on integrable systems give a comprehensive survey of modern research in this area. Algebraic and geometric aspects are dealt with, as are non-linear equations, hierarchies of equations, and quantum groups.

Автор: A.S. Fokas; I.M. Gelfand
Название: Algebraic Aspects of Integrable Systems
ISBN: 1461275350 ISBN-13(EAN): 9781461275350
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Описание: Irene Dorfman died in Moscow on April 6, 1994, shortly after seeing her beautiful book on Dirac structures I]. The present volume contains a collection of papers aiming at celebrating her outstanding contributions to mathematics. Her most important discoveries are associated with the algebraic structures arising in the study of integrable equations. Most of the articles contained in this volume are in the same spirit. Irene, working as a student of Israel Gel'fand made the fundamental dis- covery that integrability is closely related to the existence of bi-Hamiltonian structures 2], 3]. These structures were discovered independently, and al- most simultaneously, by Magri 4] (see also 5]). Several papers in this book are based on this remarkable discovery. In particular Fokas, Olver, Rosenau construct large classes on integrable equations using bi-Hamiltonian struc- tures, Fordy, Harris derive such structures by considering the restriction of isospectral flows to stationary manifolds and Fuchssteiner discusses similar structures in a rather abstract setting.

Автор: Richard H. Cushman; Larry M. Bates
Название: Global Aspects of Classical Integrable Systems
ISBN: 3034898177 ISBN-13(EAN): 9783034898171
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Описание: This book gives a complete global geometric description of the motion of the two di- mensional hannonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top.

Автор: Richard H. Cushman; Larry M. Bates
Название: Global Aspects of Classical Integrable Systems
ISBN: 3034809174 ISBN-13(EAN): 9783034809177
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Описание: This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top.

Автор: B.G. Konopelchenko
Название: Introduction to Multidimensional Integrable Equations
ISBN: 0306442205 ISBN-13(EAN): 9780306442209
Издательство: Springer
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Описание: The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis- covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans- form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.

Автор: Boris G. Konopelchenko
Название: Nonlinear Integrable Equations
ISBN: 3662136104 ISBN-13(EAN): 9783662136102
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Автор: B.G. Konopelchenko
Название: Introduction to Multidimensional Integrable Equations
ISBN: 1489911723 ISBN-13(EAN): 9781489911728
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Автор: R. Conte; N. Boccara
Название: Partially Integrable Evolution Equations in Physics
ISBN: 9401067546 ISBN-13(EAN): 9789401067546
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Описание: Proceedings of the NATO Advanced Study Institute on Partially Integrable Nonlinear Evolution Equations and Their Physical Applications, Les Houches, France, March 21-30, 1989

Автор: Mikhael Balabane; Pierre Lochak; Catherine Sulem
Название: Integrable Systems and Applications
ISBN: 366213747X ISBN-13(EAN): 9783662137475
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Описание: In this volume nonlinear systems related to integrable systems are studied. Lectures cover such topics as the application of integrable systems to the description of natural phenomena, the elaboration of perturbation theories, and the statistical mechanics of ensembles of objects obeying integrable equations. The more physical lectures center largely around the three paradigmatic equations: Korteweg de Vries, Sine-Gordon and Nonlinear Schr dinger, especially the latter. These have long been of great mathematical interest, and also exhibit a "universality" which places them among the most frequently encountered integrable equations in the description of physical systems. Tidal waves, optical fibers and laser beams are among the topics discussed. Lectures are also devoted to multidimensional solitons, integrability of Hamiltonian systems of ODEs and dissipative systems of PDEs.

Автор: Claude Albert; Robert Brouzet; Jean P. Dufour
Название: Integrable Systems and Foliations
ISBN: 1461286689 ISBN-13(EAN): 9781461286684
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Описание: The articles in this volume are an outgrowth of a colloquium "Systemes Integrables et Feuilletages," which was held in honor of the sixtieth birthday of Pierre Molino.

The topics cover the broad range of mathematical areas which were of keen interest to Molino, namely, integral systems and more generally symplectic geometry and Poisson structures, foliations and Lie transverse structures, transitive structures, and classification problems.

Автор: N. J. Hitchin
Название: Integrable Systems
ISBN: 0199676771 ISBN-13(EAN): 9780199676774
Издательство: Oxford Academ
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Описание: Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.