000 07468nam a2200805 i 4500
001 8940932
003 IEEE
005 20200413152931.0
006 m eo d
007 cr cn |||m|||a
008 191223s2020 caua fob 001 0 eng d
020 _a9781681737133
_qelectronic
020 _z9781681737140
_qhardcover
020 _z9781681737126
_qpaperback
024 7 _a10.2200/S00963ED1V01Y201910WAV002
_2doi
035 _a(CaBNVSL)mat00979859
035 _a(OCoLC)1133127431
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQA927
_b.T367 2020eb
082 0 4 _a531/.1133
_223
100 1 _aTanaka, Mitsuhiro,
_eauthor.
245 1 0 _aPhysics of nonlinear waves /
_cMitsuhiro Tanaka.
264 1 _a[San Rafael, California] :
_bMorgan & Claypool,
_c[2020]
300 _a1 PDF (xv, 237 pages) :
_billustrations (some color).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _aSynthesis lectures on wave phenomena in the physical sciences ;
_v#2
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader.
500 _aPart of: Synthesis digital library of engineering and computer science.
504 _aIncludes bibliographical references and index.
505 0 _a1. 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
505 8 _a2. 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
505 8 _a3. 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
505 8 _a4. 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
505 8 _a5. 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
505 8 _a6. 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
505 8 _a7. 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
505 8 _a8. 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
505 8 _aA. Conservation law in 3D -- A.1. Flux density vector -- A.2. Conservation law in integral form -- A.3. Conservation law of differential form
505 8 _aB. 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
505 8 _aC. Summary of Fourier analysis -- C.1. Fourier series -- C.2. Fourier transform -- C.3. Solution of the diffusion equation
505 8 _aD. 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
505 8 _aE. 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
505 8 _aF. 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
505 8 _aG. 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.
506 _aAbstract freely available; full-text restricted to subscribers or individual document purchasers.
510 0 _aCompendex
510 0 _aINSPEC
510 0 _aGoogle scholar
510 0 _aGoogle book search
520 _aThis 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.
530 _aAlso available in print.
588 _aTitle from PDF title page (viewed on December 23, 2019).
650 0 _aNonlinear waves.
653 _anonlinear wave
653 _adispersive wave
653 _awater wave
653 _asoliton
653 _amodulated wavetrain
653 _awave-wave interaction
653 _awave turbulence
655 0 _aElectronic books.
776 0 8 _iPrint version:
_z9781681737126
_z9781681737140
830 0 _aSynthesis digital library of engineering and computer science.
830 0 _aSynthesis lectures on wave phenomena in the physical sciences ;
_v#2.
856 4 2 _3Abstract with links to resource
_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=8940932
856 4 0 _3Abstract with links to full text
_uhttps://doi.org/10.2200/S00963ED1V01Y201910WAV002
999 _c562403
_d562403