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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

M·T·穆斯塔法, K·玛苏德. 具有三阶非调和修正项时非线性弹性波动方程的对称解[J]. 应用数学和力学, 2009, 30(8): 953-962. doi: 10.3879/j.issn.1000-0887.2009.08.008
引用本文: M·T·穆斯塔法, K·玛苏德. 具有三阶非调和修正项时非线性弹性波动方程的对称解[J]. 应用数学和力学, 2009, 30(8): 953-962. doi: 10.3879/j.issn.1000-0887.2009.08.008
M. T. Mustafa, Khalid Masood. Symmetry Solutions of a Non-Linear Elastic Wave Equation With Third Order Anharmonic Corrections[J]. Applied Mathematics and Mechanics, 2009, 30(8): 953-962. doi: 10.3879/j.issn.1000-0887.2009.08.008
Citation: M. T. Mustafa, Khalid Masood. Symmetry Solutions of a Non-Linear Elastic Wave Equation With Third Order Anharmonic Corrections[J]. Applied Mathematics and Mechanics, 2009, 30(8): 953-962. 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
详细信息
  • 中图分类号: O347.4+1

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

  • 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.
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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

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