This book discusses the application of nonlinear mathematical techniques to a variety of physical problems including nonlinear optics, turbulence, plasma physics and inverse scattering. It will be useful to all students and researchers wanting a survey and reference source concerning recent developments.

Inhalt
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 KdVHierarchy.- 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 inFluid 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.