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J4 ›› 2010, Vol. 45 ›› Issue (11): 122-126.

• 数学 • 上一篇    

非线性圆杆波导波动方程的显式精确解

郭鹏,万桂新,王小云,孙小伟   

  1. 兰州交通大学数理与软件工程学院, 甘肃 兰州 730070
  • 收稿日期:2009-11-18 出版日期:2010-11-16 发布日期:2010-11-24
  • 作者简介:郭鹏(1978-),男,讲师,主要从事非线性物理的研究工作.Email: guopenglzjtu@126.com
  • 基金资助:

    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)

Explicit and exact solution to a nonlinear wave equation in circular-rod waveguide

GUO Peng, WAN Gui-xin, WANG Xiao-yun, SUN Xiao-wei   

  1. School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2009-11-18 Online:2010-11-16 Published:2010-11-24

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。

关键词: 试探函数方法;非线性波;精确解

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.
 

Key words: trial function method; nonlinear wave; exact solution

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