This paper explores the propagation of nonlinear elastic waves in a two-dimensional isotropic medium. The analytical expressions of first-order potentials corresponding to second harmonic acoustic components are obtained and discussed by using the perturbation method. Based on the careful theoretical analysis, it is shown that the first-order P wave always has a resonant term, which is proportional to the propagation distance in the condition of simultaneous excitation of the P wave. On the contrary, the first-order SV wave does not have any cumulative effect. Moreover, the nonlinear interactions between the P wave and SV are also presented.

中文翻译：

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非线性弹性波的摄动方法研究

本文探讨了非线性弹性波在二维各向同性介质中的传播。利用摄动法获得并讨论了与二次谐波声学分量对应的一阶电势的解析表达式。根据认真的理论分析，可以看出一阶P波始终具有一个谐振项，该谐振项与P波同时激发的传播距离成正比。相反，一阶SV波没有任何累积效应。此外，还提出了P波和SV之间的非线性相互作用。