| 非线性圆杆波导波动方程的显式精确解 |
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| 引用本文： | 郭鹏,万桂新,王小云,孙小伟. 非线性圆杆波导波动方程的显式精确解[J]. 山东大学学报(理学版), 2010, 45(11): 122-126 |
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| 作者姓名： | 郭鹏 万桂新 王小云 孙小伟 |
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| 作者单位： | 兰州交通大学数理与软件工程学院, 甘肃 兰州 730070 |
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| 基金项目： | 甘肃省自然科学基金资助项目(0916RJZA047);兰州交通大学“青蓝”人才工程资助项目(QL-06-22A) |
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| 摘 要： | 对计入横向惯性效应后的非线性弹性圆杆波导纵向波动方程进行了分析。 通过引入试探函数, 把难于求解的非线性偏微分方程化为易于求解的代数方程,然后用待定系数法确定相应的常数,从而简洁地求得了方程的精确解。
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| 关 键 词： | 试探函数方法 非线性波 精确解, |
| 收稿时间： | 2009-11-18 |
Explicit and exact solution to a nonlinear wave equation in circular-rod waveguide |
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| GUO Peng,WAN Gui-xin,WANG Xiao-yun,SUN Xiao-wei. Explicit and exact solution to a nonlinear wave equation in circular-rod waveguide[J]. Journal of Shandong University, 2010, 45(11): 122-126 |
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| Authors: | GUO Peng WAN Gui-xin WANG Xiao-yun SUN Xiao-wei |
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| Affiliation: | School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China |
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| Abstract: | The longitudinal oscillation of a nonlinear elastic circular-rod waveguide with lateral inertia was studied. By introducing appropriate trial functions, the nonlinear partial differential equation, that is difficult to solve by the usual ways can be reduced to a set of algebraic equation, which can be easily solved, and its related coefficients can be easily determined by the method of undetermined coefficient. Finally, the analytical solution to the equation was successfully derived.
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| Keywords: | trial function method nonlinear wave exact solution |
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