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
相关论文
共 50 条
  • [21] On exact solutions of some important nonlinear conformable time-fractional differential equations
    Özkan E.M.
    Özkan A.
    SeMA Journal, 2023, 80 (2) : 303 - 318
  • [22] Backlund transformations and exact solutions for some nonlinear evolution equations in solar magnetostatic models
    Khater, AH
    Callebaut, DK
    Malfliet, W
    Kamel, ES
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 140 (1-2) : 435 - 467
  • [23] Symbolic computation of exact solutions for nonlinear evolution equations
    Lei Zhang
    Yezhi Lin
    Nonlinear Dynamics, 2015, 79 : 823 - 833
  • [24] A procedure to construct exact solutions of nonlinear evolution equations
    Adem Cengiz Çevikel
    Ahmet Bekir
    Mutlu Akar
    Sait San
    Pramana, 2012, 79 : 337 - 344
  • [25] The Lambert Function and Exact Solutions of Nonlinear Parabolic Equations
    A. A. Kosov
    E. I. Semenov
    Russian Mathematics, 2019, 63 : 10 - 16
  • [26] A Series of New Exact Solutions of Nonlinear Evolution Equations
    Abdou, M. A.
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2010, 26 (05) : 993 - 1005
  • [27] A procedure to construct exact solutions of nonlinear evolution equations
    Cevikel, Adem Cengiz
    Bekir, Ahmet
    Akar, Mutlu
    San, Sait
    PRAMANA-JOURNAL OF PHYSICS, 2012, 79 (03): : 337 - 344
  • [28] The Lambert Function and Exact Solutions of Nonlinear Parabolic Equations
    Kosov, A. A.
    Semenov, E. I.
    RUSSIAN MATHEMATICS, 2019, 63 (08) : 10 - 16
  • [29] Symbolic computation of exact solutions for nonlinear evolution equations
    Zhang, Lei
    Lin, Yezhi
    NONLINEAR DYNAMICS, 2015, 79 (02) : 823 - 833
  • [30] Exact solutions of some nonlinear systems of partial differential equations by using the first integral method
    Hosseini, K.
    Ansari, R.
    Gholamin, R.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 387 (02) : 807 - 814
12345