Nonlinear Processes in Physics: Proceedings of the III Potsdam -- V Kiev Workshop at Clarkson University, Potsdam, Ny, Usa, August 1-11, 1991

ISBN-13: 9783642777714 / Angielski / Miękka / 2011 / 343 str.

A. S. Fokas; D. J. Kaup; A. C. Newell

Opis

In 1979, a historical meeting took place at the Institute for Theoretical Physics in Kiev, USSR, where 48 American Scientists, specialists in nonlinear and turbulent processes, met for two weeks with their soviet counterparts. This meeting pro vided the unique opportunity for USA and USSR participants to directly interact personally and scientifically with each other. This interaction was of great impor not only for the individuals involved but also for the science of nonlinear tance phenomena in general. At the end of the meeting, it was agreed that this exchange should continue, and it was decided to have the next meeting in the USA in 1981. Unfortunately, due to the political situation at that time, the second meeting in the USA never materialized. However, in 1983, the Soviet scientists organized in Kiev a second Workshop. This second meeting was again quite successful. Similar meetings, with growing success were organized at Kiev in 1987, and 1989. It should be noted that 405 participants from 22 countries participated at the fourth Kiev workshop on Nonlinear and Turbulent Processes. The Chainnan of this workshop was V. Zakharov, who has also been a co-chainnan of all the previous workshops.

Spis treści

I Nonlinear Equations.- Multisoliton-like Solutions of Wave Propagation in Periodic Nonlinear Structures.- Complex Deformation of Integrable Hamiltonians over Generalized Jacobi Varieties.- Collective Coordinates by a Variational Approach: Problems for Sine Gordon and ?4 Models.- Spatiotemporal Chaos in the Nonlinear Three Wave Interaction.- On the Instability of the Static Soliton-like “Bubbles”.- Symplectic and Hamiltonian Structures of Nonlinear Evolution Equations.- A Fuchs Extension to the Painlevé Test.- Modulation Equations for Nearly Integrable PDEs with Periodic Boundary Conditions.- Spectrum of Domain Wall Excitations in YIG.- Interaction of Defects in Nonlinear Dissipative Fields.- On the Analytic Degenerate Dispersion Laws.- II Inverse Scattering Transforms.- Breaking Solitons. Systems of Hydrodynamic Type.- Real and Virtual Multidimensional Solitons.- Resolvent Approach for the Nonstationary Schrödinger Equation with Line-Type Potential.- Lattice Construction of Quantum Integrable Systems.- Combining Dressing and Nonlocality.- Initial Boundary-Value Problems for Soliton Equations.- Non-Perturbative Two-Dimensional Quantum Gravity and the Isomonodromy Method.- The Action of the Virasoro Nonisospectral KdV Symmetries of the Whitham Equations.- A Generalized Sato’s Equation of the KP Theory and Weyl Algebra.- Quasirelativistic Analogs of Lax Equations.- n × n Zakharov-Shabat System of the Form (d?/dx)(z2 ? 1/z2)J? + (zQ + P + R/z)?.- Homoclinic Orbits and Bäcklund Transformations for the Doubly Periodic Davey-Stewartson Equation.- Volterra Operator Algebra for Zero Curvature Representation Universality of KP.- Calculation of All Commutation Relations Among Scattering Data Without Using the R-Matrix Approach.- Fluctuating Solitons of the KdV Hierarchy.- The Periodic Fixed Points of Bäcklund Transformations.- IST for KPI.- III Plasmas.- A Physical Model for Nonlinear, Supersonic Equatorial Bubbles.- Nonlinear Dynamics of Electron Cyclotron Heated Plasmas.- Nonlinear Evolution of Alfvén Waves in Space Plasmas.- Alfvén Solitons and the DNLS Equation.- On the Analytical Theory for Self-Focusing of Radiation.- Ionospheric Langmuir Turbulence Driven by an Electromagnetic Pump Below the Upper-Hybrid Frequency.- Mode Conversions in Ionospheric Modification Experiments.- On the Superstrong Wave Collapse.- A Moving Boundary Problem in Plasma Physics.- Proton-Whistler Interactions in the Radiation Belts.- IV Nonlinear Optics.- Optical Turbulence in Semiconductor Lasers.- Chaotic Dynamics Due to Competition Among Degenerate Modes in a Ring-Cavity Laser.- Quantum Self Phase Modulation in Optical Fibres.- Quantum Groups: Q-Boson Theories of Integrable Models and Applications in Non-Linear Optics.- Perturbation Method and Optical Solitons.- Birefringent Optical Fibers: Modulational Instability in a Near-Integrable System.- Rigorous Results in Quantum Theory of Stimulated Raman Scattering.- Bäcklund Transformations as Physical Equations.- Level Splitting and Band Formation of Dark Soliton Eigenvalues.- Soliton Propagation in a Random Medium.- V Hydrodynamics and Turbulence.- Length Scales and the Navier-Stokes Equations.- Local and Nonlocal Transfer of Motion Integrals in Wave Turbulence.- Weak and Strong Turbulence in the CGL Equation.- Numerical Test of a Weak Turbulence Approximation for an Electromagnetically Driven Langmuir Turbulence.- Drift Wave Vortices in Inhomogeneous Plasmas.- Solitons on a Vortex Filament with Axial Flow.- Lagrangian Statistics of Turbulence.- Pattern Formation Via Resonant Interactions in Fluid Flows.- Length Scale of Vortices and Mode Competition in Quasi 2D Shear Flows.- Dynamics of Vortex-Current Filaments in MHD Plasma.- Success of Arnol’d’s Method in a Hierarchy of Ocean Models.- Wavelets and Two Dimensional Turbulence.- VI Inverse Scattering Problems.- Spectral Theory of Linear ?-Matrices and the Solution of Certain Nonlinear Algebraic and Functional Equations.- Nonlinear Acoustic Tomography.- Spectral Transform for Nonlinear Evolution Equations with N Space Dimensions.- Index of Contributors.