中文摘要：

应用增加了负幂次项的广义（G′／G）．展开法，通过构建新的辅助微分方程，构建三阶非线性波动方程新的精确解，包括双曲函数解、三角函数解、有理函数解以及负幂次解形式。本研究有助于理解松弛介质中声波的传播，以及非线性弹性杆中具有横向剪切纵波的传播。

英文摘要：

A generalized （ G′/G ）-expansion method, which add negative power exponent, and new auxiliary differential equation have been applied to construct new exact solutions of the third order nonlinear wave equation. The obtained exact solutions include hyperbolic function solutions, trigonometric function solutions, rational function solutions and negative power solutions. These solutions are helpful to understand acoustic wave propagation in relaxing media and longitudinal wave propagation with transverse shearing in nonlinear elastic bar.