Exact solutions of some general nonlinear wave equations in elasticity

A. H. Bokhari; A. H. Kara; F. D. Zaman

doi:10.1007/s11071-006-9050-z

Exact solutions of some general nonlinear wave equations in elasticity

A. H. Bokhari, A. H. Kara^*, F. D. Zaman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	49-54
Number of pages	6
Journal	Nonlinear Dynamics
Volume	48
Issue number	1-2
DOIs	https://doi.org/10.1007/s11071-006-9050-z
State	Published - Apr 2007

Bibliographical note

Funding Information:
Acknowledgements AHB and FDZ would like to thank the KFUPM for support under the Fast Track Project FT/2005-02. Also, AHK thanks the KFUPM for their support and hospitality during a visit.

Keywords

Exact solutions
Nonlinear elasticity equations
Similarity analysis

ASJC Scopus subject areas

Control and Systems Engineering
Aerospace Engineering
Ocean Engineering
Mechanical Engineering
Applied Mathematics
Electrical and Electronic Engineering

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10.1007/s11071-006-9050-z

Cite this

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abstract = "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.",

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author = "Bokhari, \{A. H.\} and Kara, \{A. H.\} and Zaman, \{F. D.\}",

note = "Funding Information: Acknowledgements AHB and FDZ would like to thank the KFUPM for support under the Fast Track Project FT/2005-02. Also, AHK thanks the KFUPM for their support and hospitality during a visit.",

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AU - Kara, A. H.

AU - Zaman, F. D.

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PY - 2007/4

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N2 - 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.

AB - 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.

KW - Exact solutions

KW - Nonlinear elasticity equations

KW - Similarity analysis

UR - https://www.scopus.com/pages/publications/33846482024

U2 - 10.1007/s11071-006-9050-z

DO - 10.1007/s11071-006-9050-z

M3 - Article

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SN - 0924-090X

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JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 1-2

ER -

Exact solutions of some general nonlinear wave equations in elasticity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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