具有三阶非调和修正项时非线性弹性波动方程的对称解

M·T·穆斯塔法; K·玛苏德

doi:10.3879/j.issn.1000-0887.2009.08.008

具有三阶非调和修正项时非线性弹性波动方程的对称解

doi: 10.3879/j.issn.1000-0887.2009.08.008

M·T·穆斯塔法¹,
K·玛苏德²

1.
法赫德国王石油矿产大学数理统计系,达兰31261,沙特阿拉伯;2.法赫德国王石油矿产大学哈菲尔阿尔_巴廷社区学院数学系,达兰 31261,沙特阿拉伯

详细信息

中图分类号: O347.4⁺¹
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出版历程
- 收稿日期: 2008-08-23
- 修回日期: 2009-03-16
- 刊出日期: 2009-08-15

Symmetry Solutions of a Non-Linear Elastic Wave Equation With Third Order Anharmonic Corrections

M. T. Mustafa¹,
Khalid Masood²

1.
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;

摘要

摘要: 应用Lie对称法，当弹性能具有三阶非调和修正项时，分析纵向变形的非线性弹性波动方程．通过不同对称下的恒等条件，寻找对称代数，并将它简化为二阶常微分方程．对该简化的常微分方程作进一步分析后，获得若干个显式的精确解．分析Apostol的研究成果(Apostol B F.On a non-linear wave equation in elasticity.Phys Lett A,2003,318(6):545-552)发现，非调和修正项通常导致解在有限时间内具有时间相关奇异性．除了得到时间相关奇异性的解外，还得到无法显示时间相关奇异性的解．
- 群不变解 /
- Lie对称 /
- 非线性弹性方程 /
- 偏微分方程 /
- 常微分方程
Abstract: Lie symmetry method was applied to analyze a non-linear elastic wave equation for longitudinal deformations with third order anharmonic corrections to the elastic energy. Symmetry algebra was found and reductions to second order ODEs were obtained through invariance under different symmetries. The reduced ODEs were further analyzed to obtain several exact solutions in explicit form. Apostol(Apostol B F. On a non-linear wave equation in elasticity. Phys Lett A, 2003, 318(6):545552) had observed that anharmonic corrections generally lead t o solutions with time-dependent singularities in finite time. Along with solutions with time-dependent singularities are obtained, also solutions which do not exhibit time-dependent singularities were obtained.
- group invariant solution /
- Lie symmetries /
- nonlinear elasticity equations /
- partial differential equations /
- ordinary differential equations

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参考文献(26)

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