• 1. Basic Equations for Wave Processes in Fluids and Solids.- 1.1 Sound in Layered Fluids.- 1.2 Harmonic Waves.- 1.3 Elastic Waves in Isotropic Solids.- 2. Plane Waves in Discretely Layered Fluids.- 2.1 Inhomogeneous Plane Waves. Energy of Sound Waves.- 2.2 Reflection at the Interface of Two Homogeneous Media.- 2.3 Locally Reacting Surfaces.- 2.4 Reflection from a Plane Layer.- 2.5 Reflection and Transmission Coefficients for an Arbitrary Number of Layers.- 2.6 Moving Layers. Impedance of Harmonic Waves in Moving Media.- 3. Monochromatic Plane-Wave Reflection from Continuously Layered Media.- 3.1 General Relations.- 3.2 Solvable Profiles k(z) from the Confluent Hypergeometric Equation.- 3.3 Solvable Profiles Obtained from the Hypergeometric Equation.- 3.4 Plane-Wave Reflection from an Epstein Layer.- 3.5 Reflection of a Plane Wave from a Half-Space with a Linear Law for the Squared Refraction Index.- 3.6 Other Cases with Exact Solutions for Normal Incidence.- 3.7 Exact Solutions for Media with Continuous Stratification of Sound Velocity, Density, and Flow Velocity.- 4. Plane-Wave Reflection from the Boundaries of Solids.- 4.1 Plane Waves in Elastic Half-Spaces with a Free Boundary.- 4.2 Reflection from Solid-Solid and Solid-Fluid Interfaces.- 4.3 Reflection from a System of Solid Layers.- 4.4 Surface and “Leaky” Waves.- 5. Reflection of Sound Pulses.- 5.1 General Relations. Law of Conservation of Integrated Pulse.- 5.2 Change of Pulse Shape upon Total Internal Reflection from a Boundary Between Two Homogeneous Media.- 5.3 Total Reflection of a Pulse in Continuously Layered Media.- 6. Universal Properties of the Plane-Wave Reflection and Transmission Coefficients.- 6.1 Symmetry with Respect to Reversion of the Wave Path.- 6.2 Analytic Properties.- 6.3 NonreflectingLayers.- 7. Acoustic Waves in Absorbing Anisotropic Media.- 7.1 Absorption of Sound.- 7.2 Anisotropic Elastic Media. Gulyaev-Bluestein Waves.- 7.3 Elastic Properties of Finely Layered Media.- 8. Geometrical Acoustics. WKB Approximation.- 8.1 The WKB Approximation and Its Range of Validity.- 8.2 Physical Meaning of the Approximate Solutions.- 8.3 Another Approach to the Ray Acoustics Approximation.- 9. The Sound Field in the Case of Turning Horizons and Resonance Interaction with a Flow.- 9.1 Reference Equation Method.- 9.2 Sound Field in the Vicinity of a Turning Point.- 9.3 Reflection from a “Potential Barrier”.- 9.4 Amplification of Sound in an Inhomogeneous Flow.- 10. Sound Reflection from a Medium with Arbitrarily Varying Parameters.- 10.1 Differential Equations for Reflection Coefficient and Impedance of a Sound Wave.- 10.2 Reflection from a Thin Inhomogeneous Layer.- 10.3 Method of Successive Approximations for Weakly Reflecting Layers.- 10.4 Reflection at Interfaces in Continuously Layered Media.- References.

"The two books are characterized by scholasticity in the analytical treatment. The analysis is rigorous and complete. This could be attributed to the 'Russian school' where both authors belong to, offering an excellent framework for the study of problems of Mathematical Physics. ...In general, the books are considered valuable for researchers interested in the mathematical modeling of wave phenomena as they provide the readers with a comprehensive coverage of practically all the analytical aspects of the forward problem of acoustic wave propagation. In addition, throughout the books, they will meet many references to non-standard issues, as the propogation in moving media and energy conservation." Michael Taroudakis, Acustica United with Acta Acus, 2000/86/6