Oscillations and Waves: in Linear and Nonlinear Systems: Mathematics and its Applications, cartea 50

One. Oscillations and Waves in Linear Systems.- 1. Linear Oscillators.- 2. Oscillations in a System with Two Linked Oscillators.- 3. Oscillations in an Ensemble of Non-Interacting Oscillators.- 4. Oscillations in Ordered Structures. Limit for a Continuous medium. Waves. Dispersion.- 5. Properties of Waves with Small Amplitudes in Continuous media.- 6. Stability and Instability of Linear Systems with Discrete Spectra.- 7. Stability of Distributed Systems with Continuous Spectra.- 8. Propagation Velocity of Waves.- 9. Energy and Momentum of Waves.- 10. Waves with Negative Energy. Linked Waves.- 11. Parametric Systems and Parametric Instability.- 12. Adiabatic Invariants. Propagation of Waves in Inhomogeneous Media.- Two. Oscillations and Waves in Nonlinear Systems.- 13. The Nonlinear Oscillator.- 14. Periodic Self-Excited Oscillations.- 15. General Properties of Nonlinear Dynamic Systems in Phase Space.- 16. Self-Excited Oscillations in Multifrequency Systems.- 17. Resonance Interactions between Oscillators.- 18. Simple Waves and the Formation of Discontinuities.- 19. Stationary Shock Waves and Solitons.- 20. Modulated Waves in Nonlinear Media.- 21. Self-Excited Oscillations in Distributed Systems.- 22. Stochastic Dynamics in Simple Systems.- 23. The Onset of Turbulence.- 24. Self-Organization.- References.