In this article, the non-linear anti-symmetric shear motion for some comparative studies between the non-homogeneous and homogeneous plates, having two free surfaces with stress-free, is considered. Assuming that one plate contains hyper-elastic, non-homogeneous, isotropic, and generalized neo-Hookean materials and the other one consists of hyper-elastic, homogeneous, isotropic, and generalized neo-Hookean materials. Using the method of multiple scales, the self-modulation of the non-linear anti-symmetric shear motion in these plates, as the non-linear Schrödinger (NLS) equations, can be given. Using the known solitary wave solutions, called bright and dark solitary wave solutions, to NLS equations, these comparative studies in terms of the non-homogeneous and non-linear effects are made. All numerical results, based on the asymptotic analyses, are graphically presented for the lowest anti-symmetric branches of both dispersion relations, including the deformation fields of plates.

在本文中，考虑了具有两个自由表面且无应力的非均质板和均质板之间的非线性反对称剪切运动，以进行一些比较研究。假设一个板包含超弹性，非均质，各向同性和广义的新霍克材料，另一块包含超弹性，均质，各向同性和广义的新霍克材料。使用多尺度方法，可以给出非线性板中非线性反对称剪切运动的自调制，作为非线性Schrödinger（NLS）方程。使用已知的孤立波解，称为明和暗孤立波解，用于NLS方程，就非均匀和非线性效应进行了这些比较研究。所有数值结果，基于渐近分析，