Nonlinear Processes In Physics: Proceedings Of The Iii Potsdam _ V Kiev Workshop At Clarkson University, Potsdam, Ny, Usa, August 1-11, 1991 (springer Series In Nonlinear Dynamics)

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. Front Matter....Pages I-XV Front Matter....Pages 1-1 Multisoliton-like Solutions of Wave Propagation in Periodic Nonlinear Structures....Pages 3-5 Complex Deformation of Integrable Hamiltonians over Generalized Jacobi Varieties....Pages 6-20 Collective Coordinates by a Variational Approach: Problems for Sine Gordon and Φ 4 Models....Pages 21-24 Spatiotemporal Chaos in the Nonlinear Three Wave Interaction....Pages 25-28 On the Instability of the Static Soliton-like “Bubbles”....Pages 29-31 Symplectic and Hamiltonian Structures of Nonlinear Evolution Equations....Pages 32-34 A Fuchs Extension to the Painlevé Test....Pages 35-44 Modulation Equations for Nearly Integrable PDEs with Periodic Boundary Conditions....Pages 45-46 Spectrum of Domain Wall Excitations in YIG....Pages 47-52 Interaction of Defects in Nonlinear Dissipative Fields....Pages 53-59 On the Analytic Degenerate Dispersion Laws....Pages 60-63 Front Matter....Pages 65-65 Breaking Solitons. Systems of Hydrodynamic Type....Pages 67-76 Real and Virtual Multidimensional Solitons....Pages 77-81 Resolvent Approach for the Nonstationary Schrödinger Equation with Line-Type Potential....Pages 82-86 Lattice Construction of Quantum Integrable Systems....Pages 87-90 Combining Dressing and Nonlocality....Pages 91-95 Initial Boundary-Value Problems for Soliton Equations....Pages 96-101 Non-Perturbative Two-Dimensional Quantum Gravity and the Isomonodromy Method....Pages 102-107 The Action of the Virasoro Nonisospectral KdV Symmetries of the Whitham Equations....Pages 108-112 A Generalized Sato’s Equation of the KP Theory and Weyl Algebra....Pages 113-113 Front Matter....Pages 65-65 Quasirelativistic Analogs of Lax Equations....Pages 114-117 n × n Zakharov-Shabat System of the Form ( dψ/dx )( z 2 − 1/ z 2 ) Jψ + ( zQ + P + R/z ) ψ ....Pages 118-121 Homoclinic Orbits and Bäcklund Transformations for the Doubly Periodic Davey-Stewartson Equation....Pages 122-125 Volterra Operator Algebra for Zero Curvature Representation. Universality of KP....Pages 126-131 Calculation of All Commutation Relations Among Scattering Data Without Using the R-Matrix Approach....Pages 132-135 Fluctuating Solitons of the KdV Hierarchy....Pages 136-138 The Periodic Fixed Points of Bäcklund Transformations....Pages 139-147 IST for KPI....Pages 148-149 Front Matter....Pages 151-151 A Physical Model for Nonlinear, Supersonic Equatorial Bubbles....Pages 153-165 Nonlinear Dynamics of Electron Cyclotron Heated Plasmas....Pages 166-168 Nonlinear Evolution of Alfvén Waves in Space Plasmas....Pages 169-174 Alfvén Solitons and the DNLS Equation....Pages 175-178 On the Analytical Theory for Self-Focusing of Radiation....Pages 179-179 Ionospheric Langmuir Turbulence Driven by an Electromagnetic Pump Below the Upper-Hybrid Frequency....Pages 180-184 Mode Conversions in Ionospheric Modification Experiments....Pages 185-190 On the Superstrong Wave Collapse....Pages 191-194 A Moving Boundary Problem in Plasma Physics....Pages 195-198 Proton-Whistler Interactions in the Radiation Belts....Pages 199-209 Front Matter....Pages 211-211 Optical Turbulence in Semiconductor Lasers....Pages 213-217 Chaotic Dynamics Due to Competition Among Degenerate Modes in a Ring-Cavity Laser....Pages 218-227 Front Matter....Pages 211-211 Quantum Self Phase Modulation in Optical Fibres....Pages 228-231 Quantum Groups: Q-Boson Theories of Integrable Models and Applications in Non-Linear Optics....Pages 232-240 Perturbation Method and Optical Solitons....Pages 241-241 Birefringent Optical Fibers: Modulational Instability in a Near-Integrable System....Pages 242-246 Rigorous Results in Quantum Theory of Stimulated Raman Scattering....Pages 247-251 Bäcklund Transformations as Physical Equations....Pages 252-255 Level Splitting and Band Formation of Dark Soliton Eigenvalues....Pages 256-260 Soliton Propagation in a Random Medium....Pages 261-264 Front Matter....Pages 265-265 Length Scales and the Navier-Stokes Equations....Pages 267-270 Local and Nonlocal Transfer of Motion Integrals in Wave Turbulence....Pages 271-274 Weak and Strong Turbulence in the CGL Equation....Pages 275-278 Numerical Test of a Weak Turbulence Approximation for an Electromagnetically Driven Langmuir Turbulence....Pages 279-280 Drift Wave Vortices in Inhomogeneous Plasmas....Pages 281-290 Solitons on a Vortex Filament with Axial Flow....Pages 291-298 Lagrangian Statistics of Turbulence....Pages 299-302 Pattern Formation Via Resonant Interactions in Fluid Flows....Pages 303-304 Length Scale of Vortices and Mode Competition in Quasi 2D Shear Flows....Pages 305-305 Dynamics of Vortex-Current Filaments in MHD Plasma....Pages 306-309 Success of Arnol’d’s Method in a Hierarchy of Ocean Models....Pages 310-314 Wavelets and Two Dimensional Turbulence....Pages 315-325 Front Matter....Pages 327-327 Spectral Theory of Linear λ-Matrices and the Solution of Certain Nonlinear Algebraic and Functional Equations....Pages 329-333 Nonlinear Acoustic Tomography....Pages 334-338 Spectral Transform for Nonlinear Evolution Equations with N Space Dimensions....Pages 339-342 Back Matter....Pages 343-344 This book gives an up-to-date survey of the application of nonlinear mathematical techniques to a variety of physical problems. Examples of the areas covered are inverse scattering, nonlinear optics, fluids, plasmas and ionoshperic physics.