## Nonlinear Wave Processes in AcousticsThe investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth of interest in nonlinear acoustic phenomena. In this book, the authors consider models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. The authors also consider the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and interaction of acoustic beams. This book will be of interest not only to specialists in acoustics, but also to a wide audience of mathematicians, physicists, and engineers working on nonlinear waves in various physical systems. |

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### Contents

Nonlinearity dissipation and dispersion in acoustics | 1 |

12 Isotropic solids | 11 |

13 Liquid with gas bubbles | 16 |

14 Elastic medium with cavities | 25 |

15 Anomalous nonlinearities in elastic media | 30 |

Simple waves and shocks in acoustics | 37 |

22 Simple waves and discontinuities | 39 |

23 Propagation of pulses | 49 |

44 Divergent waves | 150 |

45 Foci and caustics | 158 |

Soundsound interaction nondispersive medium | 165 |

52 Parametric acoustic transmitters | 176 |

53 Parametric sound reception | 188 |

Nonlinear acoustic waves in dispersive media | 198 |

62 Nonlinear waves in a waveguide | 204 |

63 Parametric amplification and generation of sound | 208 |

Burgers equation | 54 |

25 Propagation of intense acoustic noise | 61 |

26 Waves in media with anomalous nonlinearity | 72 |

27 Sound excitation and amplification by moving sources | 78 |

28 Finiteamplitude standing waves | 85 |

29 Energy and momentum in a plane sound wave | 90 |

Nonlinear geometrical acoustics | 98 |

32 Nonlinear wave evolution along the rays | 103 |

33 Spherical waves | 105 |

34 Nonlinear acoustics of explosive waves | 112 |

35 Onedimensional propagation in inhomogeneous media Waves in the atmosphere | 115 |

36 Refraction of nonlinear waves in a stratified medium | 120 |

37 Selfrefraction of shock waves | 127 |

Nonlinear sound beams | 140 |

42 The nonlinear beam equation | 142 |

43 Stepbystep technique | 148 |

64 Acoustic solitons in a liquid with gas bubbles | 217 |

65 Acoustic solitons in solids | 220 |

66 Wave interaction in a liquid with resonance bubbles | 228 |

67 Parametric sound transmitter in a waveguide | 235 |

Selfaction and stimulated scattering of sound | 245 |

72 Selffocusing of sound | 250 |

73 Onedimensional modulated waves | 255 |

74 Stimulated scattering of sound | 261 |

75 Wave front reversal | 265 |

76 Concentration nonlinearity in a liquid with gas bubbles | 273 |

77 Cavitational selffocusing of sound | 283 |

78 Phase locking of nonlinear oscillators in acoustics | 286 |

Conclusion | 295 |

297 | |

### Common terms and phrases

acoustic waves Akust amplification amplitude asymptotic average behaviour boundary condition bubbles Burgers equation Chapter characteristic chromosphere considered constant coordinate corresponding curve decay dependence described diffraction discontinuity formation dispersion dissipation distance effects energy equal evolution experimental factor field Figure finite amplitude formula function Gurbatov harmonic wave high-frequency inhomogeneous initial integral intensity interaction JASA Khokhlov layer liquid longitudinal wave low-frequency Mach number medium mode modulation Naugol'nykh nonlinear acoustics nonlinear distortions nonlinear wave nonlinearity parameter obtain oscillations Ostrovsky parametric array perturbation phase plane wave pressure problem pulse pump wave quadratic radiation radius relation resonance Reynolds number Rudenko sawtooth wave scattering second harmonic self-focusing shock front shock wave signal simple wave solitons solution Soluyan sound beam sound velocity spectrum spherical Substituting Sutin thermal transmitter variables viscosity wave amplitude wave equation wave profile wave propagation waveguide width yields Zabolotskaya