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**Nonlinear wave propagation in micropolar media. I: The general theory.**
*(English)*
Zbl 0694.73006

Summary: The plane wave propagation in nonlinear micropolar solids is asymptotically investigated. Micropolar theory in the linear approximation predicts a dispersive optical (high-frequency) mode as well as a dispersive acoustical (low-frequency) mode for the harmonic waves in an unbounded medium. The acoustical mode has a weakly dispersive region when the wave number is small. If nonlinearity is also present in this weakly dispersive region and if both effects are small but finite, it may be expected that nonlinearity and dispersive effects can balance each other, and the wave propagation can be asymptotically governed by a nonlinear evolution equation which admits a solitary wave type solution. Using the reductive perturbation method to examine the plane wave propagation in a general nonlinear polar solid, it is found that far- field approximation of wave motion is governed by coupled modified Korteweg-de Vries equations.

### MSC:

74B20 | Nonlinear elasticity |

74J20 | Wave scattering in solid mechanics |

35Q99 | Partial differential equations of mathematical physics and other areas of application |

74H45 | Vibrations in dynamical problems in solid mechanics |

74A35 | Polar materials |

### Keywords:

plane wave propagation; dispersive effects; nonlinear evolution equation; solitary wave type solution; reductive perturbation method; general nonlinear polar solid; far-field approximation of wave motion; coupled modified Korteweg-de Vries equations### Citations:

Zbl 0694.73007
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\textit{S. Erbay} and \textit{E. S. Şuhubi}, Int. J. Eng. Sci. 27, No. 8, 895--914 (1989; Zbl 0694.73006)

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### References:

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