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Journal of Applied Mathematics
Volume 2014, Article ID 487571, 10 pages
http://dx.doi.org/10.1155/2014/487571
Research Article

Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations

1School of Science, Chang’an University, Xi’an 710064, China
2School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China

Received 31 December 2013; Revised 23 March 2014; Accepted 25 March 2014; Published 22 April 2014

Academic Editor: Michael Meylan

Copyright © 2014 Shi Jing and Yan Xin-li. 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.

Abstract

The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method) can be used to solve other similar nonlinear wave equations.