Slowly Varying Oscillations And Waves: From Basics To Modernity
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A01=Lev Ostrovsky
Airy Function
Asymptotic Perturbation Methods
Author_Lev Ostrovsky
Autosolitons
Autowaves
Average Lagrangian
Burgers Equation
Category=PHDS
Cnoidal Waves
Compound Solitons
Coupled Waves
Dispersion Relation
Duffing Oscillator
Elliptic Functions
Ensembles of Solitons and Kinks
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Frequency Doubling
Gardner Equation
Geometrical Theory
Geometrical Theory of Waves
Gross-Pitaevskii Equation
Group and Phase Velocities
Internal Waves
Kadomtsev-Petviashvili Equation
Kinks
Klein-Gordon Equation
Korteweg-de Vries Equation
KPP-fisher Model
Kuramoto Model
Linear and Nonlinear
Linear and Nonlinear Oscillations and Waves
Models of Laser
Modulation Instability
Nonlinear Acoustics
Nonlinear Optics
Nonlinear Pendulum
Oscillators and Waves
Parametric Resonance
Period Doubling
Reaction-Diffusion System
Resonance
Rotational Kdv Equation
Schrodinger Equation
Self-Focusing
Self-Similar Solutions
Sine-Gordon Equation
Slowly Varying Oscillators and Waves
Soliton
Stationary Phase Method
Swift-Hohenberg Equation
Synchronization of Oscillators
Taylor Shock
Terminal Damping
Van Der Pol Oscillator
Water Waves
Wave Asymptotic
Wave Beams
Wave Trapping
Waves of Envelopes
Whitham's Theory
Product details
- ISBN 9789811247484
- Publication Date: 27 May 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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The beauty of the theoretical science is that quite different physical, biological, etc. phenomena can often be described as similar mathematical objects, by similar differential (or other) equations. In the 20th century, the notion of "theory of oscillations" and later "theory of waves" as unifying concepts, meaning the application of similar methods and equations to quite different physical problems, came into being. In the variety of applications (quite possibly in most of them), the oscillatory process is characterized by a slow (as compared with the characteristic period) variation of its parameters, such as the amplitude and frequency. The same is true for the wave processes.This book describes a variety of problems associated with oscillations and waves with slowly varying parameters. Among them the nonlinear and parametric resonances, self-synchronization, attenuated and amplified solitons, self-focusing and self-modulation, and reaction-diffusion systems. For oscillators, the physical examples include the van der Pol oscillator and a pendulum, models of a laser. For waves, examples are taken from oceanography, nonlinear optics, acoustics, and biophysics. The last chapter of the book describes more formal asymptotic perturbation schemes for the classes of oscillators and waves considered in all preceding chapters.
