非线性弹性杆波动方程的显式精确解  

Explicit Exact Solutions to the Wave Equation for Nonlinear Elastic Rods

作　　者：郭鹏 唐荣安[4] 孙小伟[2] 洪学仁[4] 石玉仁[4] GUO Peng;TANG Rongan;SUN Xiaowei;HONG Xueren;SHI Yuren(School of Materials Science and Engineering,Lanzhou Jiaotong University,Lanzhou 730070,P.R.China;School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,P.R.China;Key Laboratory of Railway Vehicle Thermal Engineering,Ministry of Education,Lanzhou Jiaotong University,Lanzhou 730070,P.R.China;College of Physics and Electronic Engineering,Northwest Normal University,Lanzhou 730070,P.R.China)

机构地区：[1]兰州交通大学材料科学与工程学院,兰州730070 [2]兰州交通大学数理学院,兰州730070 [3]兰州交通大学铁道车辆热工教育部重点实验室,兰州730070 [4]西北师范大学物理与电子工程学院,兰州730070

出　　处：《应用数学和力学》2022年第8期869-876,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11765017,12065022,12165018);甘肃省重点人才项目(2020RCXM100)。

摘　　要：应用sine-cosine方法对非线性弹性杆波动方程进行了求解,得到了该方程的一些新的周期波解和孤波解(材料常数n为不等于1的常数).对部分结果通过数学软件得到了解的图像,获得的结果有助于非线性弹性杆中孤波存在性问题的进一步研究.The sine-cosine method was applied to the wave equation for nonlinear elastic rods,and some new periodic and solitary solutions to the equation were obtained(with material constant n other than 1).The graphs of some solutions were given through the math software.The results are helpful to further research on existence of solitary waves in the nonlinear elastic rods.

关 键 词：sine-cosine方法 非线性弹性杆 精确解 孤波 

分 类 号：O343[理学—固体力学] O175.2[理学—力学]