电磁弹性圆杆中纵波方程的新波动性
On the new wave behavior to the longitudinal wave quation in a magneto-electro-elastic circular rod
摘要：
借助符号计算软件Wolfram Mathematica 9，采用功能强大的sine-Gordon展开法，研究了磁电弹性圆杆中纵波方程的解析解。Sine-Gordon展开法是基于著名的sine-Gordon方程和一种波变换。纵波方程是在数学物理中产生的方程，其具有由磁电弹性圆杆中的横向泊松效应引起的色散。我们成功地得到了一些具有复、三角和双曲函数结构的解。通过选择适当的参数值，我们给出了所有得到的解决方案的数值模拟。给出了某些解析解的物理意义，这些解析解对一些实际物理问题有重要的解释作用。
英文摘要：
With the aid of the symbolic computations software; Wolfram Mathematica 9, the powerful sine-Gordon expansion method is used in examining the analytical solution of the longitudinal wave equation in a magneto-electro-elastic circular rod. Sine-Gordon expansion method is based on the well-known sine-Gordon equation and a wave transformation. The longitudinal wave equation is an equation that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic circular rod. We successfully get some solutions with the complex, trigonometric and hyperbolic function structure. We present the numerical simulations of all the obtained solutions by choosing appropriate values of the parameters. We give the physical meanings of some of the obtained analytical solutions which significantly explain some practical physical problems.
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