Table of Contents Author Guidelines Submit a Manuscript
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.

Linked References

  1. Z. F. Liu and S. Y. Zhang, “Solitary waves in finite deformation elastic circular rod,” Journal of Applied Mathematics and Mechanics, vol. 27, no. 10, pp. 1255–1260, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. E. V. Krishnan, S. Kumar, and A. Biswas, “Solitons and other nonlinear waves of the Boussinesq equation,” Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, vol. 70, no. 2, pp. 1213–1221, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Biswas, M. Song, H. Triki et al., “Solitons, Shockwaves, conservation laws and bifurcation analysis of boussinesq equation with power law nonlinearity and dual-dispersion,” Journal of Applied Mathematics and Information Science, vol. 8, no. 3, pp. 949–957, 2014. View at Google Scholar
  4. A. Ja'afar, M. Jawad, M. D. Petkovic, and A. Biswas, “Soliton solutions to a few coupled nonlinear wave equations by tanh method,” The Iranian Journal of Science and Technology A, vol. 37, no. 2, pp. 109–115, 2013. View at Google Scholar
  5. J. F. Zhang, “Multi-solitary wave solutions for variant Boussinesq equations and Kupershmidt equations,” Journal of Applied Mathematics and Mechanics, vol. 21, no. 2, pp. 171–175, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Zhang, Q. Liu, J. Wang, and K. Wu, “A new supersymmetric classical Boussinesq equation,” Chinese Physics B, vol. 17, no. 1, pp. 10–16, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. Y. B. Yuan, D. M. Pu, and S. M. Li, “Bifurcations of travelling wave solutions in variant Boussinesq equations,” Journal of Applied Mathematics and Mechanics, vol. 27, no. 6, pp. 716–726, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Sirendaoreji and S. Jiong, “Auxiliary equation method for solving nonlinear partial differential equations,” Physics Letters A, vol. 309, no. 5-6, pp. 387–396, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Taogetusang and Sirendaoreji, “New types of exact solitary wave solutions for (2+1)-dimensional dispersive long-wave equations and combined KdV-Burgers equation,” Chinese Journal of Engineering Mathematics, vol. 23, no. 5, pp. 943–946, 2006. View at Google Scholar · View at MathSciNet
  10. E. G. Fan and H. Q. Zhang, “Solitary wave solutions of a class of nonlinear wave equations,” Acta Physica Sinica, vol. 46, no. 7, pp. 1254–1258, 1997. View at Google Scholar · View at MathSciNet
  11. W. L. Zhang, G. J. Wu, M. Zhang, J. M. Wang, and J. H. Han, “New exact periodic solutions to (2+1)-dimensional dispersive long wave equations,” Chinese Physics B, vol. 17, no. 4, pp. 1156–1164, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Bartoszewski, “Solving boundary value problems for delay differential equations by a fixed-point method,” Journal of Computational and Applied Mathematics, vol. 236, no. 6, pp. 1576–1590, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. T. Fu, S. K. Liu, S. D. Liu, and Q. Zhao, “New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations,” Physics Letters A, vol. 290, no. 1-2, pp. 72–76, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. L. Wang, Y. B. Zhou, and Z. B. Li, “Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics,” Physics Letters A: General, Atomic and Solid State Physics, vol. 216, no. 1–5, pp. 67–75, 1996. View at Google Scholar · View at Scopus
  15. E. G. Fan and H. Q. Zhang, “The homogeneous balance method for solving nonlinear soliton equations,” Acta Physica Sinica, vol. 47, no. 3, pp. 353–362, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. D. Liu, Z. T. Fu, S. K. Liu, and Q. Zhao, “Enveloping periodic solutions to nonlinear wave equations with Jacobi elliptic functions,” Acta Physica Sinica, vol. 51, no. 4, pp. 718–722, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. A. J. M. Jawad, M. D. Petković, P. Laketa, and A. Biswas, “Dynamics of shallow water waves with Boussinesq equation,” Scientia Iranica B, vol. 20, no. 1, pp. 179–184, 2013. View at Google Scholar
  18. X. L. Yan, “Existence and uniqueness theorems of solution for symmetric contracted operator equations and their applications,” Chinese Science Bulletin, vol. 36, no. 10, pp. 800–805, 1991. View at Google Scholar · View at MathSciNet
  19. J. P. Hao and X. L. Yan, “Exact solution of large deformation basic equations of circular membrane under central force,” Journal of Applied Mathematics and Mechanics, vol. 27, no. 10, pp. 1169–1172, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. X. L. Yan, Exact Solution of Nonlinear Equations, Economic Scientic Press, Beijing, China, 2004.
  21. Y.-Z. Peng, “Exact solutions for some nonlinear partial differential equations,” Physics Letters A, vol. 314, no. 5-6, pp. 401–408, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. L. X. Gong, “Some new exact solutions via the Jacobi elliptic functions to the nonlinear Schrödinger equation,” Acta Physica Sinica, vol. 55, no. 9, pp. 4414–4419, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet