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Symmetric bright solitary SH waves in a nonlinear heterogeneous plate

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Abstract

In this work, we investigate the propagation of shear horizontal (SH) waves in a nonlinear hyperelastic plate. We assume that the plate is made of heterogeneous, isotropic, and generalized neo-Hookean materials. The problem is examined with a perturbation method that balances the nonlinearity and dispersion in the analysis. Then, a nonlinear Schrödinger (NLS) equation is derived describing the nonlinear self-modulation of the waves. Using known solutions of an NLS equation, we found that the symmetric bright solitary SH waves will exist and propagate in this plate. Moreover, not only the effect of the heterogeneity, but also the effect of the nonlinearity on the deformation field is also considered for these waves.

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  1. Beykent University, Buyukcekmece Campus, 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 bright solitary SH waves in a nonlinear heterogeneous plate. Z. Angew. Math. Phys. 70, 63 (2019). https://doi.org/10.1007/s00033-019-1108-0

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  • DOI: https://doi.org/10.1007/s00033-019-1108-0

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