Oscillations and Waves in Linear and Nonlinear Systems [Paperback]

One. Oscillations and Waves in Linear Systems.- 1. Linear Oscillators.- 1.1. General Notes.- 1.2. Two Examples. The Phase Plane Diagram of an Oscillator.- 1.3. Resonance. The Effect of an Aperiodic External Force on an Oscillator.- 1.4. Normal Oscillations. Analogy with Quantum Mechanics. Production and Extinction Operators.- 2. Oscillations in a System with Two Linked Oscillators.- 2.1. Initial Equations.- 2.2. The Fundamental Oscillations of Two Linked Oscillators.- 2.3. Disturbance of Two Linked Oscillators by an External Force. The Reciprocity Principle.- 3. Oscillations in an Ensemble of Non-Interacting Oscillators.- 3.1. Classical Theory of Dispersion.- 3.2. Oscillations in an Ensemble of Dissimilar Noninteracting Oscillators with a Given Distribution Function.- 4. Oscillations in Ordered Structures. Limit for a Continuous medium. Waves. Dispersion.- 4.1. General Remarks.- 4.2. Oscillations in Ordered Structures (Chains of Linked Particles and Identical Linked Oscillators).- 4.3. Limiting Transition from an Ordered Structure to a One-dimensional Medium. Temporal and Spatial Dispersion. Physical Nature of Dispersion.- 4.4. Typical Dispersion Characteristics for Medium Models.- 4.5. Formal Method for Obtaining the Dispersion Equation. Waves in a One-Dimensional Resonator. Resonance in Wave Systems.- 5. Properties of Waves with Small Amplitudes in Continuous media.- 5.1. General Remarks.- 5.2. Equations of Hydrodynamics. Dispersion for Sound Waves. For Sound Waves.- 5.3. A Stratified Fluid. Sound in an Ocean.- 5.4. Gravity Waves in an Incompressible Liquid. Internal Waves. Rossby Waves.- 5.5. Waves in a Superfluid Liquid.- 5.6. Waves in a Plasma. Hydrodynamic Description.- 6. Stability and Instability of Linear Systems with Discrete Spectra.- 6.1. General Notes and Definitions.- 6.2. The Raus-Gurvits Criterion and Three-Dimensional Systems.- 6.3. The D-Partition Method.- 6.4. Stability of Non-Autonomous Systems.- 6.5. Instability Mechanisms.- 7. Stability of DistlCH