扩展的极简(G′/G)展开法获取杆中非线性波动方程的精确解及分析  

The exact solution and analysis of the nonlinear waveequation in the rod obtained by the extendedminimal ( G′/G ) expansion method

作　　者：范凯[1] 刘健康 孙宝[1] 李占龙[2] FAN Kai;LIU Jiankang;SUN Bao;LI Zhanlong(School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China;School of Vehicle and Traffic Engineering,Taiyuan University of Science and Technology,Taiyuan 030024,China)

机构地区：[1]太原科技大学应用科学学院,太原030024 [2]太原科技大学车辆与交通工程学院,太原030024

出　　处：《重庆理工大学学报（自然科学）》2023年第6期294-300,共7页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(52272401);山西省基础研究计划项目(202203021221150);山西省高等学校科技创新项目(2022L301);太原科技大学科研启动基金项目(20222076)。

摘　　要：对扩展的(G′/G)展开法进行等价简化,将2个Ricatti方程的精确解耦合为非线性波动方程的精确解。使用扩展的极简(G′/G)展开法获取非线性波动方程的26个精确解,发现耦合解中不仅分布有极简(G′/G)法与极简(G/G′)法获取的精确解,还存在新形式的精确解。对讨论得到的位移梯度解u_(13,14)及对应的应变波函数,代入材料参数进行数值模拟,发现扭结孤立波和钟状应变波,且杆半径越大,对材料的抗拉强度要求越高。This paper firstly conducts equivalent simplification of the extended(G′/G)expansion method and proposes to couple the exact solutions of the two Ricatti equations into the exact solutions of the nonlinear wave equation.Secondly,26 exact solutions of the nonlinear wave equation are obtained by using the extended minimalist(G′/G)expansion method.It is found that not only exact solutions obtained by the minimalist(G′/G)method and the minimalist(G/G′)method are distributed among the coupling solutions,but a new form of the exact solutions also exists.Finally,the displacement gradient solutions u 13,14 obtained in this study and their corresponding strain wave function are brought into the material parameters for numerical simulation,and both kink isolated waves and bell strain waves are found.The analysis shows that the larger the radius of the rod,the higher the tensile strength of the material.

关 键 词：非线性波动方程 扩展的(G′/G)展开法 行波解 孤立波解 

分 类 号：O175[理学—数学]