### Abstract

Gaussian wave packets are high frequency, asymptotic solutions to the equations of elastodynamics. They can be used, for example, to model pulse propagation in complex materials with smoothly varying properties and sharp surfaces of material discontinuity. The fundamental departure from the usual geometrical optics development is that the phase function is assumed to be complex valued. This has important consequences for the behaviour of the solution in the neighbourhood of the unique central ray. For example, if the initial disturbance is in the shape of a gaussian envelope, the propagated pulse remains gaussian. Nonlinear effects are taken into account by assuming the strains remain small, so that weakly nonlinear wave theory can be used. A nonlinear phase modulation equation is derived; and solved for an initial disturbance corresponding to an acceleration wave. This example illustrates that one can obtain a much richer theory through the use of complex phase.

Original language | English (US) |
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Title of host publication | North-Holland Series in Applied Mathematics and Mechanics |

Pages | 491-504 |

Number of pages | 14 |

Edition | C |

DOIs | |

State | Published - Jan 1 1989 |

### Publication series

Name | North-Holland Series in Applied Mathematics and Mechanics |
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Number | C |

Volume | 35 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Computational Mechanics

### Cite this

*North-Holland Series in Applied Mathematics and Mechanics*(C ed., pp. 491-504). (North-Holland Series in Applied Mathematics and Mechanics; Vol. 35, No. C). https://doi.org/10.1016/B978-0-444-87272-2.50079-8

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*North-Holland Series in Applied Mathematics and Mechanics.*C edn, North-Holland Series in Applied Mathematics and Mechanics, no. C, vol. 35, pp. 491-504. https://doi.org/10.1016/B978-0-444-87272-2.50079-8

**Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids.** / Norris, Andrew N.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids

AU - Norris, Andrew N.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - Gaussian wave packets are high frequency, asymptotic solutions to the equations of elastodynamics. They can be used, for example, to model pulse propagation in complex materials with smoothly varying properties and sharp surfaces of material discontinuity. The fundamental departure from the usual geometrical optics development is that the phase function is assumed to be complex valued. This has important consequences for the behaviour of the solution in the neighbourhood of the unique central ray. For example, if the initial disturbance is in the shape of a gaussian envelope, the propagated pulse remains gaussian. Nonlinear effects are taken into account by assuming the strains remain small, so that weakly nonlinear wave theory can be used. A nonlinear phase modulation equation is derived; and solved for an initial disturbance corresponding to an acceleration wave. This example illustrates that one can obtain a much richer theory through the use of complex phase.

AB - Gaussian wave packets are high frequency, asymptotic solutions to the equations of elastodynamics. They can be used, for example, to model pulse propagation in complex materials with smoothly varying properties and sharp surfaces of material discontinuity. The fundamental departure from the usual geometrical optics development is that the phase function is assumed to be complex valued. This has important consequences for the behaviour of the solution in the neighbourhood of the unique central ray. For example, if the initial disturbance is in the shape of a gaussian envelope, the propagated pulse remains gaussian. Nonlinear effects are taken into account by assuming the strains remain small, so that weakly nonlinear wave theory can be used. A nonlinear phase modulation equation is derived; and solved for an initial disturbance corresponding to an acceleration wave. This example illustrates that one can obtain a much richer theory through the use of complex phase.

UR - http://www.scopus.com/inward/record.url?scp=85023321721&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85023321721&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/B978-0-444-87272-2.50079-8

DO - https://doi.org/10.1016/B978-0-444-87272-2.50079-8

M3 - Chapter

T3 - North-Holland Series in Applied Mathematics and Mechanics

SP - 491

EP - 504

BT - North-Holland Series in Applied Mathematics and Mechanics

ER -