Symmetry solutions of a nonlinear elastic wave equation with third-order anharmonic corrections

被引：0
|
作者：
M. Tahir Mustafa
Khalid Masood
机构：
[1] King Fahd University of Petroleum and Minerals,Department of Mathematics and Statistics
[2] King Fahd University of Petroleum and Minerals,Department of Mathematics, Hafr Al
来源：
Applied Mathematics and Mechanics | 2009年 / 30卷
关键词：
group invariant solutions; Lie symmetries; nonlinear elasticity equations; partial differential equations; O151.23; 76M60; 73C50; 74J30; 74H05;
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学科分类号：
摘要：
Lie symmetry method is applied to analyze a nonlinear elastic wave equation for longitudinal deformations with third-order anharmonic corrections to the elastic energy. Symmetry algebra is found and reductions to second-order ordinary differential equations (ODEs) are obtained through invariance under different symmetries. The reduced ODEs are further analyzed to obtain several exact solutions in an explicit form. It was observed in the literature that anharmonic corrections generally lead to solutions with time-dependent singularities in finite times. Along with solutions with time-dependent singularities, we also obtain solutions which do not exhibit time-dependent singularities.
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页码：1017 / 1026
页数：9
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