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慢变振荡和波动：从基础到现代（英文版）
作者：暂缺
出版社：高等教育出版社
出版时间：2021-12-01
ISBN：9787040558029
定价：¥199.00
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内容简介
完全不同的物理、生物等现象常常可以用相似的微分（或其他）方程描述为类似的数学对象，这就是理论科学的美妙之处。在20世纪，“振荡理论”和后来的“波动理论”作为统一的概念出现了，这意味着相似的方法和方程可以应用于完全不同的物理问题。在各种应用中（很可能在大多数应用中），振荡过程的特征是其参数（如振幅和频率）的缓慢变化（与特征周期相比）。波动过程也是如此。本书描述了与振荡和慢变参数波有关的各种问题。其中包括非线性和参数共振、自同步、衰减和放大孤子、自聚焦和自调制以及反应扩散系统。对于振荡器，物理例子包括van der Pol振荡器和钟摆，它们是激光器的模型。对于波，例子来自海洋学、非线性光学、声学和生物物理学。本书的最后一章描述了前面所有章节中考虑的振荡器和波类的更形式化的渐近摄动格式。
作者简介
列夫·奥斯特洛夫斯基（Lev Ostrovsky），是科罗拉多大学博尔德分校应用数学系兼职教授。他的研究兴趣广泛，包括非线性流体力学、非线性海洋学理论等。他曾获得苏联国家奖、俄罗斯科学院Mandelstam奖、非线性科学与复杂性委员会Lagrange奖和苏联发现奖（Diploma），目前已出版了3本专著，发表了300多篇论文。
目录
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
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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