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Integrable Systems and Applications

Proceedings of a Workshop Held at Oléron, France, June 20–24, 1988

  • Conference proceedings
  • © 1989

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Editors:
  1. M. Balabane
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  2. P. Lochak
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  3. C. Sulem
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Part of the book series: Lecture Notes in Physics (LNP, volume 342)

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Table of contents (25 papers)

  1. Front Matter

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  2. Global solutions to non linear Dirac equations in Minkowski space

    • Alain Bachelot
    Pages 1-11

  3. Statistical mechanics of the NLS models and their avatars

    • R. K. Bullough, Yu-zhong Chen, S. Olafsson, J. Timonen
    Pages 12-26

  4. Asymptotic behavior of solutions and universal attractors for a system of nonlinear hyperbolic equations

    • Piotr Biler
    Pages 27-30

  5. Solitons in two dimensions

    • M. Boiti, J. JP. Leon, L. Martina, F. Pempinelli
    Pages 31-48

  6. Nonlinear wave propagation through a random medium and soliton tunneling

    • J. G. Caputo, A. C. Newell, M. Shelley
    Pages 49-64

  7. Trace formulae and singular spectra for the Schrödinger operator

    • Walter Craig
    Pages 65-81

  8. Hunting of the quarton

    • Anthony P. Csizmazia
    Pages 82-86

  9. Nekhoroshev's theorem and particle channeling in crystals

    • H. Scott Dumas
    Pages 87-94

  10. Linearized maps for the Davey-Stewartson I equation

    • A. S. Fokas
    Pages 95-104

  11. On the role of nonlinearities in classical electrodynamics

    • Luigi Galgani
    Pages 105-112

  12. Upper bounds on the Lyapunov exponents for dissipative perturbations of infinite dimensional Hamiltonian systems

    • Jean-Michel Ghidaglia
    Pages 113-126

  13. The Cauchy problem for the generalized Korteweg-de-Vries equation

    • J. Ginibre
    Pages 127-141

  14. Effective stability in Hamiltonian systems in the light of Nekhoroshev's theorem

    • Antonio Giorgilli
    Pages 142-153

  15. Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system

    • Manoussos Grillakis
    Pages 154-191

  16. On numerical chaos in the nonlinear Schrödinger equation

    • B. M. Herbst, Mark J. Ablowitz
    Pages 192-206

  17. Singular solutions of the cubic Schrödinger equation

    • M. J. Landman, B. J. LeMesurier, G. C. Papanicolaou, C. Sulem, P. L. Sulem
    Pages 207-217

  18. Hamiltonian deformations and optical fibers

    • Curtis R. Menyuk
    Pages 218-231

  19. The Josephson fluxon mechanics

    • G. Reinisch, J. C. Fernandez
    Pages 232-260

  20. Real lattices modelled by the nonlinear Schrödinger equation and its generalizations

    • Michel Remoissenet
    Pages 261-270
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Keywords

About this book

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 Schrödinger, 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.

Bibliographic Information

  • Book Title: Integrable Systems and Applications

  • Book Subtitle: Proceedings of a Workshop Held at Oléron, France, June 20–24, 1988

  • Editors: M. Balabane, P. Lochak, C. Sulem

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/BFb0035656

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-662-13747-5Published: 23 August 2014

  • eBook ISBN: 978-3-540-46714-4Published: 11 April 2006

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: VII, 344

  • Number of Illustrations: 24 b/w illustrations

  • Topics: Quantum Physics, Quantum Information Technology, Spintronics, Analysis

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