完全不同的物理、生物等現(xiàn)象常?？梢杂孟嗨频奈⒎郑ɑ蚱渌┓匠堂枋鰹轭愃频臄?shù)學(xué)對象，這就是理論科學(xué)的美妙之處。在20世紀(jì)，“振蕩理論”和后來的“波動(dòng)理論”作為統(tǒng)一的概念出現(xiàn)了，這意味著相似的方法和方程可以應(yīng)用于完全不同的物理問題。在各種應(yīng)用中（很可能在大多數(shù)應(yīng)用中），振蕩過程的特征是其參數(shù)（如振幅和頻率）的緩慢變化（與特征周期相比）。波動(dòng)過程也是如此。本書描述了與振蕩和慢變參數(shù)波有關(guān)的各種問題。其中包括非線性和參數(shù)共振、自同步、衰減和放大孤子、自聚焦和自調(diào)制以及反應(yīng)擴(kuò)散系統(tǒng)。對于振蕩器，物理例子包括van der Pol振蕩器和鐘擺，它們是激光器的模型。對于波，例子來自海洋學(xué)、非線性光學(xué)、聲學(xué)和生物物理學(xué)。本書的最后一章描述了前面所有章節(jié)中考慮的振蕩器和波類的更形式化的漸近攝動(dòng)格式。
Preface Introduction Chapter 1 Perturbed Oscillations 1.1 Linear Oscillator with Damping 1.2 Oscillator with Cubic Nonlinearity 1.3 Oscillator Under the Action of External Force. Resonance 1.4 A Forced Nonlinear Oscillator 1.5 Oscillators with Variable Parameters. Parametric Resonance 1.5.1 Slowly varying parameters. WKB approximation 1.5.2 Parametric resonance 1.6 Active Systems. The van der Pol Oscillator 1.7 A Lumped Model of Laser 1.8 Strongly Nonlinear Oscillators. A Pendulum 1.8.1 Ideal pendulum 1.8.2 Damping oscillations 1.9 A Charged Particle in the Magnetic Field 1.10 Interaction of Nonlinear Oscillators 1.11 Synchronization 1.11.1 Coupled Duffing oscillators 1.11.2 Synchronization of active oscillators 1.12 Self-Synchronization in Ensembles of Oscillators 1.12.1 Synchronization of limit cycles. Kuramoto model 1.12.2 Auto-synchronization of Duffing oscillators 1.13 Variable-Parameter Chaotic Oscillations Appendix A. The Jacobi Elliptic Functions Appendix B. Phase Plane References Chapter 2 Linear Waves 2.1 Kinematics of Waves. Phase and Group Velocity 2.2 Klein-Gordon Equation with Dissipation 2.2.1 Non-dissipative KG equation 2.2.2 KG with dissipation 2.3 Linear SchrSdinger Equation 2.3.1 General form 2.3.2 Gaussian impulse 2.4 Evolution of Wave Amplitude and Wavenumber 2.4.1 General equations 2.4.2 Self-similar solutions 2.4.3 Fresnel integrals 2.5 Asymptotic Behavior of Linear Waves 2.5.1 Method of stationary phase 2.5.2 Airy function 2.6 Wave Beams 2.6.1 Monochromatic beams 2.6.2 Space-time beams 2.7 Frequency-Modulated Dispersive Waves: Compression and Spreading 2.7.1 Space-time rays 2.7.2 Variation of wave energy and amplitude 2.7.3 Asymptotic of the envelope waves 2.8 Example: Water Waves 2.8.1 Dispersion relation 2.8.2 Deep-water waves 2.8.3 Shallow-water waves 2.9 Geometrical Theory of Waves 2.9.1 General relations 2.9.2 Geometrical acoustics 2.9.3 One-dimensional propagation. Waves in the atmosphere …… Chapter 3 Nonlinear Quasi-Harmonic Waves Chapter 4 Modulated Non-Sinusoidal Waves Chapter 5 Slowly Varying Solitons Chapter 6 Interactions of Solitons, Kinks, and Vortices Chapter 7 Fast and Slow Motions. Autowaves Chapter 8 Direct Asymptotic Perturbation Theory Epilogue Index
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