以下为句子列表：
英文: Based on the semi-vector wave equation under cylindrical coordinate system, the mode distribution and complex propagation constant in bent waveguides were computed by a finite difference method with perfectly matched layer (PML) boundary condition.
中文: 摘要以柱坐标下的半矢量波动方程为基础，采用基于完美匹配层(PML)边界条件的有限差分方法，对弯曲波导进行模式求解，进而得到波导弯曲引起的辐射损耗。
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英文: Based on the wave equation in unsaturated soil, the dynamic response of a pile under transient torsional loading was theoretically investigated.
中文: 摘要基于己建立的非饱和土中的波动方程，研究了瞬间扭转荷载作用下桩的动力响应问题。
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英文: In this paper, for proving the efficiency of the best perturbation method in getting the parameter of partial differential equations, the parameter inverse problem of one dimensional wave equation is studied based on the best perturbation method, so as to
中文: 摘要为了验证最佳摄动量法在偏微分方程参数反演中的有效性，基于最佳摄动量法研究了一维波动方程参数反问题，得出了此类问题的数值解法。
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英文: The global fast dynamics for the generalized symmetric regularized long wave equation is considered.
中文: 摘要考虑了对称正则长波方程的整体快变动力学。
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英文: Wang Shoudong, Wu Lu,Crosshole Seismic Data Image Using Wave Equation Inversion, Presented at 66th SEG Annual Meeting, 1996.
中文: 王守东，刘家琦，层状介质二维波动方程叠前反演方法，中国地球物理学会年刊，长沙，1993。
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