| Description |
1 online resource (xv, 237 pages) : illustrations (some color) |
| Series |
Synthesis lectures on wave phenomena in the physical sciences ; #2 |
|
Synthesis lectures on wave phenomena in the physical sciences ; #2
|
| Contents |
1. The simplest nonlinear wave equation -- 1.1. The simplest wave equation -- 1.2. From conservation law to wave equation -- 1.3. Method of characteristics -- 1.4. Intersection of characteristics and occurrence of multivaluedness -- 1.5. Shock fitting -- 1.6. References |
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2. Burgers equation : effect of diffusion -- 2.1. Burgers equation -- 2.2. Diffusion effect -- 2.3. Hopf-Cole transformation : close relation to diffusion equation -- 2.4. Typical solutions of the Burgers equation -- 2.5. References |
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3. Basics of linear water waves -- 3.1. Dispersion relation -- 3.2. Linear sinusoidal wave solution of water wave -- 3.3. Wave energy and its propagation velocity -- 3.4. Extension of linear solution to nonlinear solution -- 3.5. References |
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4. Perturbation method and multiple scale analysis -- 4.1. Necessity of approximate solution method -- 4.2. Perturbation method -- 4.3. Application to nonlinear pendulum -- 4.4. Multiple scale analysis -- 4.5. References |
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5. KdV equation : effect of dispersion -- 5.1. KdV equation and its intuitive derivation -- 5.2. Solitary wave solution : balance between nonlinearity and dispersion -- 5.3. Soliton : solitary wave with particle nature -- 5.4. Relatives of KdV equation -- 5.5. Whitham equation and wave breaking -- 5.6. References |
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6. Modulation and self-interaction of a wavetrain -- 6.1. Modulated or quasi-monochromatic wavetrain -- 6.2. Group velocity -- 6.3. Nonlinear Schrödinger equation : equation governing modulation -- 6.4. Modulational instability -- 6.5. References |
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7. Resonant interaction between waves -- 7.1. Three-wave interaction -- 7.2. Three-wave interaction equation -- 7.3. Wave generation and excitation by three-wave resonance -- 7.4. Special types of three-wave resonance -- 7.5. Four-wave resonant interaction -- 7.6. References |
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8. Wave turbulence : interaction of innumerable waves -- 8.1. Energy spectrum -- 8.2. Statistics about wave height -- 8.3. Evolution equation of energy spectrum -- 8.4. Power law appearing in energy spectrum -- 8.5. References |
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A. Conservation law in 3D -- A.1. Flux density vector -- A.2. Conservation law in integral form -- A.3. Conservation law of differential form |
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B. System of simultaneous wave equations -- B.1. Hyperbolic equation -- B.2. Mechanism of temporal evolution of hyperbolic system -- B.3. Riemann invariant -- B.4. Simple wave -- B.5. References |
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C. Summary of Fourier analysis -- C.1. Fourier series -- C.2. Fourier transform -- C.3. Solution of the diffusion equation |
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D. Derivation of governing equations for water waves -- D.1. Mass conservation law -- D.2. Equation of motion -- D.3. Lagrangian derivative -- D.4. Kelvin's circulation theorem -- D.5. Potential flow and Bernoulli's theorem -- D.6. References |
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E. Summary to dimensional analysis -- E.1. Dimension and SI system -- E.2. Physical quantities with independent dimensions -- E.3. Conversion of unit system -- E.4. Pi theorem -- E.5. Drag on an object by dimensional analysis -- E.6. References.215 |
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F. Derivation of the KdV equation for water waves -- F.1. The basic equations -- F.2. Derivation of long wave equation -- F.3. Derivation of the KdV equation -- F.4. References |
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G. FPU recurrence and the KdV equation -- G.1. Normal mode of oscillation -- G.2. FPU recurrence -- G.3. Derivation of the KdV equation for nonlinear lattice -- G.4. References |
| Summary |
This is an introductory book about nonlinear waves. It focuses on two properties that various different wave phenomena have in common, the "nonlinearity" and "dispersion", and explains them in a style that is easy to understand for first-time students. Both of these properties have important effects on wave phenomena. Nonlinearity, for example, makes the wave lean forward and leads to wave breaking, or enables waves with different wavenumber and frequency to interact with each other and exchange their energies. Dispersion, for example, sorts irregular waves containing various wavelengths into gentler wavetrains with almost uniform wavelengths as they propagate, or cause a difference between the propagation speeds of the wave waveform and the wave energy. Many phenomena are introduced and explained using water waves as an example, but this is just a tool to make it easier to draw physical images. Most of the phenomena introduced in this book are common to all nonlinear and dispersive waves. This book focuses on understanding the physical aspects of wave phenomena, and requires very little mathematical knowledge. The necessary minimum knowledges about Fourier analysis, perturbation method, dimensional analysis, the governing equations of water waves, etc. are provided in the text and appendices, so even second- or third-year undergraduate students will be able to fully understand the contents of the book and enjoy the fan of nonlinear wave phenomena without relying on other books |
| Analysis |
nonlinear wave |
|
dispersive wave |
|
water wave |
|
soliton |
|
modulated wavetrain |
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wave-wave interaction |
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wave turbulence |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Title from PDF title page (viewed on December 23, 2019) |
| Subject |
Nonlinear waves.
|
|
Nonlinear waves
|
| Form |
Electronic book
|
| ISBN |
1681737132 |
|
9781681737133 |
|
9783031026119 |
|
303102611X |
