Mathematics-Dynamical Systems

Integrable Systems and Applications: Proceedings of a Workshop Held at Oléron, France June 20–24, 1988

US$5.00 US$64.00

Title (user) : Integrable Systems and Applications: Proceedings of a Workshop Held at Oléron, France June 20–24, 1988Title (google) : Integrable systems and applications proceedings of a workshop, held at Oléron, France, June...
Description

Title (user) : Integrable Systems and Applications: Proceedings of a Workshop Held at Oléron, France June 20–24, 1988

Title (google) : Integrable systems and applications proceedings of a workshop, held at Oléron, France, June 20-24, 1988

ISBN : 9780387516158,0387516158,3540516158

DDC : 515/.353

LCC : QA377 .I54 1989

DOI : 10.1007/BFb0035656

GoogleBook ID : dr1ztAEACAAJ

OpenLibrary ID : OL2207357M

Series : Lecture Notes in Physics 342

Authors (user) : Alain Bachelot (auth.), M. Balabane, P. Lochak, C. Sulem (eds.)

Authors (google) : Mikhael Balabane

Publisher : Springer Berlin Heidelberg

Language : English

Publication Date : 1989

Scanned : yes (300 DPI)

File Format : djvu

Categories : Mathematics


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Description (user) :
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.


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Description (google) :
This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.


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Table of contents :
Global solutions to non linear Dirac equations in Minkowski space....Pages 1-11
Statistical mechanics of the NLS models and their avatars....Pages 12-26
Asymptotic behavior of solutions and universal attractors for a system of nonlinear hyperbolic equations....Pages 27-30
Solitons in two dimensions....Pages 31-48
Nonlinear wave propagation through a random medium and soliton tunneling....Pages 49-64
Trace formulae and singular spectra for the Schrödinger operator....Pages 65-81
Hunting of the quarton....Pages 82-86
Nekhoroshev's theorem and particle channeling in crystals....Pages 87-94
Linearized maps for the Davey-Stewartson I equation....Pages 95-104
On the role of nonlinearities in classical electrodynamics....Pages 105-112
Upper bounds on the Lyapunov exponents for dissipative perturbations of infinite dimensional Hamiltonian systems....Pages 113-126
The Cauchy problem for the generalized Korteweg-de-Vries equation....Pages 127-141
Effective stability in Hamiltonian systems in the light of Nekhoroshev's theorem....Pages 142-153
Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system....Pages 154-191
On numerical chaos in the nonlinear Schrödinger equation....Pages 192-206
Singular solutions of the cubic Schrödinger equation....Pages 207-217
Hamiltonian deformations and optical fibers....Pages 218-231
The Josephson fluxon mechanics....Pages 232-260
Real lattices modelled by the nonlinear Schrödinger equation and its generalizations....Pages 261-270
Modulation of trapped waves giving approximate two-dimensional solitions....Pages 271-281
Solvable nonlinear equations as concrete realizations of the same abstract algebra....Pages 282-294
Properties of solutions of dispersive equations....Pages 295-311
Multichannel nonlinear scattering theory for nonintegrable equations....Pages 312-327
On the linear stability of solitary waves in Hamiltonian systems with symmetry....Pages 328-335
Nonlinear Schrödinger equations with magnetic field effect: Existence and stability of solitary waves....Pages 336-342

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