具有三阶非调和修正项时非线性弹性波动方程的对称解  

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

作　　者：M·T·穆斯塔法 K·玛苏德 黄锋(译) 张禄坤(校) 

机构地区：[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 [3]不详

出　　处：《应用数学和力学》2009年第8期953-962,共10页Applied Mathematics and Mechanics

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 anon-linear wave equationin 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.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 syrmnetries. 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） ：545-552） had observed that anhannordc corrections generally lead to solutions with time-dependent singu- larities in firtite time. Along with solutions with time-dependent singularities are obtained, also solutions which do not exhibit time-dependent singularities were obtained.

关 键 词：群不变解 LIE对称 非线性弹性方程 偏微分方程 常微分方程 

分 类 号：O347.41[理学—固体力学]