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Journal of Applied Mathematics
Volume 2014, Article ID 495125, 7 pages
Research Article

New Solutions of Elastic Waves in an Elastic Rod under Finite Deformation

Peng Guo,1,2,3 Xiang Wu,2,3 and Liangbi Wang2,3

1School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China
2School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
3Key Laboratory of Railway Vehicle Thermal Engineering, Lanzhou Jiaotong University, Ministry of Education, Lanzhou 730070, China

Received 28 May 2014; Revised 19 August 2014; Accepted 19 August 2014; Published 1 September 2014

Academic Editor: Baolin Wang

Copyright © 2014 Peng Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The nonlinear wave equation of an elastic rod under finite deformation is solved by the extended mapping method. Abundant new exact traveling wave solutions for this equation are obtained, which contain trigonometric function solutions, solitary wave solutions, Jacobian elliptic function solutions, and Weierstrass elliptic function solutions. The method can be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.