In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

中文翻译：

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纵波方程孤子解及磁电弹性圆棒动力学模型研究

在本文中，我们使用改进的改进扩展tanh函数方法获得了磁电弹性圆棒非线性纵波方程的精确解。借助这种方法，我们得到了明亮奇异孤子、有理奇异周期、双曲线、雅可比椭圆函数和指数解等许多精确解。此外，还绘制了一些解的二维和三维图形，以了解物理解释。