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Solitons and Chaos

  • Conference proceedings
  • © 1991

Overview

Editors:
  1. Ioannis Antoniou

    1. Dienst Theoretische Natuurkunde (TENA), Vrije Universiteit Brussel, Brussels, Belgium

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  2. Franklin J. Lambert

    1. Dienst Theoretische Natuurkunde (TENA), Vrije Universiteit Brussel, Brussels, Belgium

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Research Reports in Physics (RESREPORTS)

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Table of contents (43 papers)

  1. Front Matter

    Pages I-XVI
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  2. General Questions on Chaos and Integrability

    1. Front Matter

      Pages 1-1
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    2. Integration of Non-Integrable Systems

      • I. Prigogine, T. Petrovsky, H. Hasegawa, S. Tasaki
      Pages 3-24

    3. Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions

      • R. K. Bullough, Yu-zhong Cheng, J. Timonen
      Pages 25-36

    4. Soliton Dynamics and Chaos Transition in a Microstructured Lattice Model

      • M. K. Sayadi, J. Pouget
      Pages 37-45

    5. What is the Role of Dynamical Chaos in Irreversible Processes?

      • P. Gaspard
      Pages 46-57

    6. A Propositional Lattice for the Logic of Temporal Predictions

      • H. Atmanspacher
      Pages 58-70

    7. Damping, Quantum Field Theory and Thermodynamics

      • E. Celeghini, M. Rasetti, G. Vitiello
      Pages 71-75

    8. Quasi-Monomial Transformations and Decoupling of Systems of ODE’s

      • L. Brenig, A. Gorielly
      Pages 76-81

  3. Physical Systems with Soliton Ingredients

    1. Front Matter

      Pages 83-83
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    2. Solitons in Optical Fibers: First- and Second-Order Perturbations

      • D. J. Kaup
      Pages 85-98

    3. Similarity Solutions of Equations of Nonlinear Optics

      • P. Winternitz
      Pages 99-107

    4. Heisenberg Ferromagnet, Generalized Coherent States and Nonlinear Behaviour

      • V. G. Makhankov
      Pages 108-110

    5. Integrable Supersymmetric Models and Phase Transitions in One Dimension

      • O. K. Pashaev
      Pages 111-114

    6. Denaturation of DNA in a Toda Lattice Model

      • P. Christiansen, A. C. Scott, P. S. Lomdahl, V. Muto
      Pages 115-122

  4. Dissipative Systems

    1. Front Matter

      Pages 123-123
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    2. A Simple Method to Obtain First Integrals of Dynamical Systems

      • R. Conte, M. Musette
      Pages 125-128

    3. Transition to Turbulence in 1-D Rayleigh-Bénard Convection

      • F. Daviaud, M. Bonetti, M. Dubois
      Pages 129-134

    4. Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow

      • E. A. Christensen, J. N. Sørensen, M. Brøns, P. L. Christiansen
      Pages 135-137

    5. Spatial Coherent Structures in Dissipative Systems

      • G. Dewel, P. Borckmans
      Pages 138-141
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Keywords

About this book

"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.

Editors and Affiliations

  • Dienst Theoretische Natuurkunde (TENA), Vrije Universiteit Brussel, Brussels, Belgium

    Ioannis Antoniou, Franklin J. Lambert

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