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In Memoriam
Prof. Alexander G. Bagdoev; Preface; Contents; 1 Waves in a Viscous Solid with Cavities; 1.1 Introduction; 1.2 Statement of the Problem and the Basic Equations; 1.3 Derivation of the Evolution Equation; 1.4 The Soliton Solution of the Evolution Equation of the Fifth Order; 1.5 Derivation of the Modulation Equation for Diffraction and One-Dimensional Problems in the Case of Quasimonochromatic Waves; 1.6 Problem Statement about Wave Fields in the Case of a Layer; 1.7 A Diffraction Problem for Narrow Beams; 1.8 Boundary Conditions
1.9 The Equation of Dimensionless Width of a Beam for Nonparaxial Rays1.10 The Solution of the Equation for Dimensionless Width of a Beam for Paraxial Rays; 1.11 The Analysis of Solutions for Narrow Beams; 1.12 Transition to an One-Dimensional Case. The Analysis of Dispersion Properties of Plane Waves; 1.13 Derivation of Evolution Equations by the Method of Bound Normal Waves; 1.14 Phase-Group Synchronism of Low-Frequency and High-Frequency Waves; 1.15 Nonlinear Stationary Waves; 2 Waves in Viscous, Dispersive, Nonlinear, Preliminary Deformable Layer with a Free Surface; 2.1 Introduction
2.2 The General Basic Equations2.3 Equilibrium Waves; 2.4 Derivation of Evolution Equations; 2.5 The Equation of Modulation and Its Solution for Narrow Bunches; 2.6 Bistability; 2.7 The ``Frozen'' Waves; 3 Waves in Solids with Porosity Filled by an Electrically Non-conducting Liquid (Biot Medium); 3.1 Introduction; 3.2 The Reference Review; 3.3 Derivation of Nonlinear Equations from the Variational Principle; 3.4 Nonlinear One-Dimensional Waves; 3.5 The Evolution Equation for a Two-Phase Medium
3.6 The Nonlinear Equation of Modulation and the Dispersion Equation with Account of Nonlinearities3.7 Solution of the Evolution and Modulation Equations; 3.8 Nonlinear Waves in a Porous Liquid-Filled Medium with Cavities; 3.9 The Equations of Deformation of the Two-Phase Biot Medium, with Account of the Temperature of both Phases; 3.10 The Linear Dispersion Equation with Account of Temperature Effects and Its Solution; 4 Waves in a Solid with Porosity Filled by Electrically Conducting Liquid Located in a Constant Electric Field; 4.1 Introduction; 4.2 Basic Equations; 4.3 One-Dimensional Case
4.4 The Linear Dispersion Equation and Its Solution4.5 Evolution Equation; 4.6 Derivation of the Schrödinger Equation and the Dispersion Nonlinear Equation; 4.7 Solutions of the Evolution and Schrödinger Equations; 5 Piesoelastic Waves; 5.1 Introduction; 5.2 The Initial Equations of Deformation of a Piezoelectric Medium; 5.3 The Equations of Deformation of Piezodielectrics with Ball Heterogeneities; 5.4 Derivation of the Modulation Equation From the Initial Equations for Piezoelectric with Ball Heterogeneities; 5.5 The Linear Dispersion Equation and Its Analysis
Prof. Alexander G. Bagdoev; Preface; Contents; 1 Waves in a Viscous Solid with Cavities; 1.1 Introduction; 1.2 Statement of the Problem and the Basic Equations; 1.3 Derivation of the Evolution Equation; 1.4 The Soliton Solution of the Evolution Equation of the Fifth Order; 1.5 Derivation of the Modulation Equation for Diffraction and One-Dimensional Problems in the Case of Quasimonochromatic Waves; 1.6 Problem Statement about Wave Fields in the Case of a Layer; 1.7 A Diffraction Problem for Narrow Beams; 1.8 Boundary Conditions
1.9 The Equation of Dimensionless Width of a Beam for Nonparaxial Rays1.10 The Solution of the Equation for Dimensionless Width of a Beam for Paraxial Rays; 1.11 The Analysis of Solutions for Narrow Beams; 1.12 Transition to an One-Dimensional Case. The Analysis of Dispersion Properties of Plane Waves; 1.13 Derivation of Evolution Equations by the Method of Bound Normal Waves; 1.14 Phase-Group Synchronism of Low-Frequency and High-Frequency Waves; 1.15 Nonlinear Stationary Waves; 2 Waves in Viscous, Dispersive, Nonlinear, Preliminary Deformable Layer with a Free Surface; 2.1 Introduction
2.2 The General Basic Equations2.3 Equilibrium Waves; 2.4 Derivation of Evolution Equations; 2.5 The Equation of Modulation and Its Solution for Narrow Bunches; 2.6 Bistability; 2.7 The ``Frozen'' Waves; 3 Waves in Solids with Porosity Filled by an Electrically Non-conducting Liquid (Biot Medium); 3.1 Introduction; 3.2 The Reference Review; 3.3 Derivation of Nonlinear Equations from the Variational Principle; 3.4 Nonlinear One-Dimensional Waves; 3.5 The Evolution Equation for a Two-Phase Medium
3.6 The Nonlinear Equation of Modulation and the Dispersion Equation with Account of Nonlinearities3.7 Solution of the Evolution and Modulation Equations; 3.8 Nonlinear Waves in a Porous Liquid-Filled Medium with Cavities; 3.9 The Equations of Deformation of the Two-Phase Biot Medium, with Account of the Temperature of both Phases; 3.10 The Linear Dispersion Equation with Account of Temperature Effects and Its Solution; 4 Waves in a Solid with Porosity Filled by Electrically Conducting Liquid Located in a Constant Electric Field; 4.1 Introduction; 4.2 Basic Equations; 4.3 One-Dimensional Case
4.4 The Linear Dispersion Equation and Its Solution4.5 Evolution Equation; 4.6 Derivation of the Schrödinger Equation and the Dispersion Nonlinear Equation; 4.7 Solutions of the Evolution and Schrödinger Equations; 5 Piesoelastic Waves; 5.1 Introduction; 5.2 The Initial Equations of Deformation of a Piezoelectric Medium; 5.3 The Equations of Deformation of Piezodielectrics with Ball Heterogeneities; 5.4 Derivation of the Modulation Equation From the Initial Equations for Piezoelectric with Ball Heterogeneities; 5.5 The Linear Dispersion Equation and Its Analysis