This volume contains most of the papers presented in the oral session of the 7th Kyoto Summer Institute (KSI) . on Dynamical Problems in Soliton Systems, held in Kyoto from August 27 to 31, 1984. Furthermore, it contains contributions of R. K. Bullough, H. H. Chen, A. S. Davydov, and N. Sanchez, who unfortunately could not attend. Thirty-six papers were presented in the oral session and 17 papers in the poster session. The meeting brought together 109 physicists and mathematicians, of which 22 were from abroad (see group photograph). The KSI is an international meeting organized by the…mehr
This volume contains most of the papers presented in the oral session of the 7th Kyoto Summer Institute (KSI) . on Dynamical Problems in Soliton Systems, held in Kyoto from August 27 to 31, 1984. Furthermore, it contains contributions of R. K. Bullough, H. H. Chen, A. S. Davydov, and N. Sanchez, who unfortunately could not attend. Thirty-six papers were presented in the oral session and 17 papers in the poster session. The meeting brought together 109 physicists and mathematicians, of which 22 were from abroad (see group photograph). The KSI is an international meeting organized by the Research Institute for Fundamental Physics (RIFP), Kyoto University to discuss various cur re nt problems of fundamental importance in theoretical physics. The 7th KSI was the first international meeting on solitons in Japan. Early in 1983, it was feit in the RIFP that the time was ripe for a conference dealing with problems concerning solitons. The RIFP asked us to organize the confer ence. The Organizing Committee consisted of: R. Hirota (Hiroshima) T. Taniuti (Nagoya) Y. H. Ichikawa (Nagoya) M. Toda (Tokyo) Z. Maki (Kyoto) M. Wadati (Tokyo) N. Yajima ( Fukuoka) S. Takeno (Kyoto) Since its discovery, the study of the soliton as a stable particle-like state of nonlinear systems has caught the imagination of physicists and mathemati cians.
I Mathematical Theory of Solitons.- Some Aspects of Soliton Dynamics.- Approximations for the Inverse Scattering Transform.- Hamiltonian Structures of Soliton Equations via Constrained Variational Calculus.- Perturbative Studies of the Zakharov-Shabat Scattering Problem.- The Zabolotskaya-Khokhlov Equation and the Inverse Scattering Problem of Classical Mechanics.- Fundamental Properties of the Binary Operators in Soliton Theory and Their Generalization.- On an Exactly Solvable Nonlinear Diffusion Equation.- Hirota's Method and the Painlevé Property.- A New Approach to Completely Integrable Partial Differential Equations by Means of the Singularity Analysis.- II Field Theory and Statistical Mechanics of Solitons.- Quantum Inverse Scattering Method.- Yang-Baxter Algebras and Integrable Models in Field Theory and Statistical Mechanics.- Solitons in the Quantum Toda Lattice.- Recent Progress in Quantum Inverse Scattering Method - Baxter Hierarchy and Its Applications.- Quantum Three Wave Interaction Models: Bethe Ansatz and Statistical Mechanics.- Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations.- Classical Statistical Mechanics of Ìntegrable Systems.- Correlation Functions of the Non-Ideal Gas of Sine-Gordon Solitons.- Classical Solutions for the Grassmannian Sigma Models and Their Supersymmetric Versions.- Einstein Equations, Non-Linear Sigma Models and Self-Dual Yang-Mills Theory.- III Solitons in Plasma Physics and Hydrodynamics.- Soliton Resonance in Plasmas.- Equilibrium Solutions in a Nonlinear Dispersive System with Instability and Damping.- Exact Solutions of Two-Dimensional Vortex Systems in Statistical Equilibrium.- Regular and Chaotic Motion of Two-Dimensional Point Vortices.- Explode-DecaySolitons.- IV Solitons in Condensed Matter Physics.- A Field Theorist's View of Conducting Polymers: Solitons in Polyacetylene and Related Systems.- Soliton, Polaron, Phonons in Polyacetylene and Their Interactions.- Soliton-like Excitations and Their Interactions in the Continuum Model of Polyacetylene.- Lattice Relaxation Theory of Soliton and Polaron Generation in Polyacetylene.- Breathers in the PPP Model of Polyacetylene.- On the Nonlinear Excitations in One-Dimensional Uniaxial Anisotropic Heisenberg Ferromagnetic Spin Chain in External Magnetic Fields.- V Solitons in Biological Systems.- Solitons and Excitons in Quasi-One-Dimensional Systems.- Biological Solitons.- Experiments for the Detection of Solitons in Biopolymers.- Solitary Excitations in DNA Double Helices.- VI Solitons and Chaos.- Pattern Selection and Low-Dimensional Chaos in Systems of Coupled Nonlinear Oscillators.- Solitons and Chaos in the Sine-Gordon System.- Soliton Propagation Properties in a Josephson Transmission Line.- A Soliton as an Attractor of a Driven Damped Nonlinear Schrödinger Equation.- Kinks and Spatially Complex Behavior in One-Dimensional Coupled Map Lattices.- Photograph of the Participants of the Seminar.- Index of Contributors.
I Mathematical Theory of Solitons.- Some Aspects of Soliton Dynamics.- Approximations for the Inverse Scattering Transform.- Hamiltonian Structures of Soliton Equations via Constrained Variational Calculus.- Perturbative Studies of the Zakharov-Shabat Scattering Problem.- The Zabolotskaya-Khokhlov Equation and the Inverse Scattering Problem of Classical Mechanics.- Fundamental Properties of the Binary Operators in Soliton Theory and Their Generalization.- On an Exactly Solvable Nonlinear Diffusion Equation.- Hirota's Method and the Painlevé Property.- A New Approach to Completely Integrable Partial Differential Equations by Means of the Singularity Analysis.- II Field Theory and Statistical Mechanics of Solitons.- Quantum Inverse Scattering Method.- Yang-Baxter Algebras and Integrable Models in Field Theory and Statistical Mechanics.- Solitons in the Quantum Toda Lattice.- Recent Progress in Quantum Inverse Scattering Method - Baxter Hierarchy and Its Applications.- Quantum Three Wave Interaction Models: Bethe Ansatz and Statistical Mechanics.- Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations.- Classical Statistical Mechanics of Ìntegrable Systems.- Correlation Functions of the Non-Ideal Gas of Sine-Gordon Solitons.- Classical Solutions for the Grassmannian Sigma Models and Their Supersymmetric Versions.- Einstein Equations, Non-Linear Sigma Models and Self-Dual Yang-Mills Theory.- III Solitons in Plasma Physics and Hydrodynamics.- Soliton Resonance in Plasmas.- Equilibrium Solutions in a Nonlinear Dispersive System with Instability and Damping.- Exact Solutions of Two-Dimensional Vortex Systems in Statistical Equilibrium.- Regular and Chaotic Motion of Two-Dimensional Point Vortices.- Explode-DecaySolitons.- IV Solitons in Condensed Matter Physics.- A Field Theorist's View of Conducting Polymers: Solitons in Polyacetylene and Related Systems.- Soliton, Polaron, Phonons in Polyacetylene and Their Interactions.- Soliton-like Excitations and Their Interactions in the Continuum Model of Polyacetylene.- Lattice Relaxation Theory of Soliton and Polaron Generation in Polyacetylene.- Breathers in the PPP Model of Polyacetylene.- On the Nonlinear Excitations in One-Dimensional Uniaxial Anisotropic Heisenberg Ferromagnetic Spin Chain in External Magnetic Fields.- V Solitons in Biological Systems.- Solitons and Excitons in Quasi-One-Dimensional Systems.- Biological Solitons.- Experiments for the Detection of Solitons in Biopolymers.- Solitary Excitations in DNA Double Helices.- VI Solitons and Chaos.- Pattern Selection and Low-Dimensional Chaos in Systems of Coupled Nonlinear Oscillators.- Solitons and Chaos in the Sine-Gordon System.- Soliton Propagation Properties in a Josephson Transmission Line.- A Soliton as an Attractor of a Driven Damped Nonlinear Schrödinger Equation.- Kinks and Spatially Complex Behavior in One-Dimensional Coupled Map Lattices.- Photograph of the Participants of the Seminar.- Index of Contributors.
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