Exact solutions of some general nonlinear wave equations in elasticity

被引：16
|
作者：
Bokhari, A. H.
Kara, A. H. [1 ]
Zaman, F. D.
机构：
[1] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, Johannesburg, South Africa
[2] Univ Witwatersrand, Ctr Differential Equat Continuum Mech & Applicat, ZA-2050 Johannesburg, Johannesburg, South Africa
[3] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia
来源：
NONLINEAR DYNAMICS | 2007年 / 48卷 / 1-2期
关键词：
similarity analysis; exact solutions; nonlinear elasticity equations;
D O I：
10.1007/s11071-006-9050-z
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
A similarity analysis of a nonlinear wave equation in elasticity is studied; in particular, one with anharmonic corrections. The symmetry transformation give rise to exact solutions via the method of invariants. In some cases, graphical figure of the solutions are presented. Furthermore, we consider some cases wherein the velocities of the longitudinal and transversal plane waves are variable. Finally, a brief discussion on how a symmetry analysis on a perturbation of the elasticity equation can be pursued.
引用
收藏
页码：49 / 54
页数：6
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