| 一类超弹性杆波动方程行波解的研究 |
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| 引用本文： | 田现东,张大珩.一类超弹性杆波动方程行波解的研究[J].三峡大学学报(自然科学版),2007,29(5):474-476. |
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| 作者姓名： | 田现东 张大珩 |
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| 作者单位： | 1. 临沂师范学院数学系,山东,临沂,276005
2. 江苏大学非线性科学研究中心,江苏,镇江,212013 |
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| 摘 要： | 讨论了一类新型的弹性杆波动方程(即非线性超弹性杆波动方程)的行波解.根据零点因子定理利用行波法把非线性超弹性杆波动方程转化成常微分方程形式并得到此类方程解的对称及反对称的性质.通过讨论方程的极限零点与非极限零点和方程解的正负变化得到非线性超弹性杆波动方程行波解存在的唯一充分条件.
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| 关 键 词： | 超弹性杆波动方程 行波解 周期解 尖波解 |
| 文章编号： | 1672-948X（2007）05-0474-03 |
| 修稿时间： | 2007-05-31 |
Research on Traveling Wave Solution of a Hyperelastic Rod Wave Equation |
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| Tian Xiandong,Zhang Dahang.Research on Traveling Wave Solution of a Hyperelastic Rod Wave Equation[J].Journal of China Three Gorges University(Natural Sciences),2007,29(5):474-476. |
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| Authors: | Tian Xiandong Zhang Dahang |
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| Institution: | 1.Department of Mathematics,Linyi Normal Univ.,Linyi 276005,China;2.Center of Nonlinear Research,Jiangsu Univ.,Zhenjiang 212013,China |
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| Abstract: | A new type of elastic rod wave equation,nonlinear hyperelastic rod wave equation,is researched.According to zero-factor theorem,the equation can be transferred into an ordinary equation;and the symmetrical and unsymmetrical properties of solution can be obtained via traveling approach.By discussing the limiting zero and unlimited zero point and the positive or negative of solution,some sufficient conditions that guarantee the existence and uniqueness of traveling wave solutions of this equation are obtained. |
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| Keywords: | hyperelastic rod wave equation traveling wave solution periodic solution peakons |
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