We investigate the self-modulation of Love waves propagating in a nonlinear half-space covered by a nonlinear layer. We assume that the constituent material of the layer is nonlinear, homogeneous, isotropic, compressible, and hyperelastic, whereas for the half-space, it is nonlinear, heterogeneous, compressible and a different hyperelastic material. By employing the nonlinear thin layer approximation, the problem of wave propagation in a layered half-space is reduced to the one for a nonlinear heterogeneous half-space with a modified nonlinear homogeneous boundary condition on the top surface. This new problem is analyzed by a relevant perturbation method, and a nonlinear Schrödinger (NLS) equation defining the self-modulation of waves asymptotically is obtained. The dispersion relation is derived for different heterogeneous properties of the half-space and the thin layer. Then the results of the thin layer approximation are compared with the ones for the finite layer obtained in Teymur et al. (Int J Eng Sci 85:150–162, 2014). The solitary solutions of the derived NLS equation are obtained for selected real material models. It has been discussed how these solutions are influenced by the heterogeneity of the semi-infinite space.

我们研究了在非线性层覆盖的非线性半空间中传播的勒夫波的自调制。我们假设层的组成材料是非线性、均匀、各向同性、可压缩和超弹性的，而对于半空间，它是非线性、异质、可压缩和不同的超弹性材料。通过采用非线性薄层近似，层状半空间中的波传播问题被简化为顶面上具有修正的非线性齐次边界条件的非线性异质半空间的问题。通过相关的微扰方法对这一新问题进行了分析，得到了渐近定义波自调制的非线性薛定谔（NLS）方程。针对半空间和薄层的不同异质性质推导了色散关系。然后将薄层近似的结果与 Teymur 等人获得的有限层结果进行比较。（国际工程杂志 85：150–162，2014 年）。对于选定的真实材料模型，获得了导出的 NLS 方程的孤立解。已经讨论了这些解如何受到半无限空间的异质性的影响。