Nonlinear Waves in Waveguides

1. Introduction.- 1.1 General Remarks.- 1.2 Overview.- 2. The Discrimination and Interaction of Hydrodynamical Waves of Different Types.- 2.1 Hydrodynamic Wave Equations in a Three-Dimensional Stratified Medium.- 2.1.1 Fundamentals.- 2.1.2 Atmospheric Waves: Dispersion and Polarization.- 2.2 Projection Operators on Subspaces of Waves.- 2.2.1 Determination of Wave Type.- 2.2.2 Projection Operators in Geophysical Hydrodynamics.- 2.2.3 Projection Operators for Poincare and Rossby Waves.- 2.3 Interaction of Surface Poincare and Rossby Waves.- 2.4 Long Atmospheric Internal Waves.- 2.4.1 Internal Waves in an Atmospheric Waveguide.- 2.5 The Method of Successive Approximations.Solution for the Cauchy Problem of the Coupled Korteweg-de Vries Equations.- 2.6 The Coupled KdV Equations.- 2.6.1 Quasisolitons of CKdV.- 2.6.2 The Symmetry and Integrability of CKdV.- 2.6.3 The Stationary Solutions of CKdV.- 2.7 Nonlinear Rossby Waves on a Sphere.- 3. Interaction of Modes in an Electromagnetic Field Waveguide.- 3.1 Electromagnetic Fields in Dielectric Waveguides.- 3.1.1 Basic Equations and Boundary Conditions.- 3.1.2 Waveguide Modes.- 3.2 Equations of Mode Interaction.- 3.3 Three-Wave Interaction of Magnetic Modes in an Extended System of Nuclear Spins.- 3.4 Nonlinear Mode Dispersion in Dielectric Waveguides.- 4. Nonlinear Waves in Stratified Plasma.- 4.1 Wave Modes in Stratified Plasma.- 4.1.1 Description of Plasma Waves.- 4.1.2 Weakly Inhomogeneous Bounded Plasma.- 4.2 Interaction of Plasma Waves.- 4.2.1 Langmuir and Ion Wave Interactions.- 4.2.2 Three-Wave Helico-Acoustic Interaction.- 4.3 Statistical Averaging and Weak Turbulence in Plasma.- 4.3.1 Spectral Densities of Electromagnetic Field Fluctuations.- 4.3.2 One-Dimensional Turbulence.- 4.4 Multisoliton Solutions of Discrete Silin-Tikhonchuk Equations.- 4.4.1 The Darboux-Matveev Transformation.- 5. Evolution Equations for Internal Waves in Media with Strongly Inhomogeneous Stratification.- 5.1 Waves in a Medium with Varying Stratification.- 5.2 Analogues of the KdV and KP Equations with Nonlocal Dispersion.- 5.3 Quasi-Waveguide Propagation of Internal Waves in the Atmosphere.- 5.4 Waves in Gases Inhomogeneous in Knudsen Number.- 6. Mean Field Generation by Waves in a Dissipative Medium.- 6.1 Description of a Wave-Medium System by the Scales of Motion.- 6.2 Thermoactivity and Diffusion in the Presence of Waves.- 6.3 Reaction of Ionosphere Plasma to a Passing Internal Wave ....- 6.4 Interaction of Internal Waves with a Dissipative Medium.- 6.4.1 Temperature Field Instability Induced by an Internal Wave.- 6.4.2 Nonsingular Perturbation Theory.- 6.5 Mean Field Generation in a Dissipative Medium and Fine Structure of the Oceanic Thermoclyne.- Appendix 1 Atmospheric Waves over a Rotating Planet.- Appendix 2 Nonlinear Terms for Interacting Modes of Poincare and Rossby Waves at a Rotating Channel Surface.- Appendix 3 Projection to the Eigen Subspaces for Acoustic and Internal Waves.- Appendix 4 Basis Vectors, Interaction Operator for Atomic Nuclei with Spin 1.- Appendix 5 Nonlinear Internal Waves and Shear Flow Interaction Constants.- References.