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Symmetric dark solitary SH waves in a nonlinear heterogeneous plate

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Abstract

In the present work, we search for the propagation of nonlinear shear horizontal waves (SH) in a finite thickness plate which consists of heterogeneous, isotropic, and generalized neo-Hookean materials. In the analysis, we apply the method of multiple scales and strike a balance between the nonlinearity and the dispersion. Then, the self-modulation of nonlinear SH waves can be given by a nonlinear Schrödinger equation which has the well-known dark solitary solution. Consequently, we show that the dark solitary SH waves can propagate in this plate. Moreover, we take the effects of heterogeneity and the nonlinearity into account for these waves.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Letters, Beykent University, 34550, Buyukcekmece, Istanbul, Turkey

    Dilek Demirkuş

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  1. Dilek Demirkuş
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Correspondence to Dilek Demirkuş.

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Demirkuş, D. Symmetric dark solitary SH waves in a nonlinear heterogeneous plate. Z. Angew. Math. Phys. 70, 108 (2019). https://doi.org/10.1007/s00033-019-1152-9

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  • DOI: https://doi.org/10.1007/s00033-019-1152-9

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