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

作　　者：M.Tahir Mustafa Khalid Masood 

机构地区：[1]Department of Mathematics and Statistics,King Fahd University of Petroleum and Minerals,Dhahran 31261, Saudi Arabia [2]Department of Mathematics, Hafr Al-Batin Community College, King Fahd University of Petroleum and Minerals,P. O. Box 5087, Dhahran 31261, Saudi Arabia

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第8期1017-1026,共10页应用数学和力学（英文版）

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 singularities, we also obtain solutions which Along with solutions with time-dependent do not exhibit time-dependent singularities.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 singularities, we also obtain solutions which Along with solutions with time-dependent do not exhibit time-dependent singularities.

关 键 词：group invariant solutions Lie symmetries nonlinear elasticity equations partial differential equations 

分 类 号：O175[理学—数学]