- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 268902, 5 pages
New Exact Solutions for a Generalized Double Sinh-Gordon Equation
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
Received 26 June 2013; Revised 15 July 2013; Accepted 15 July 2013
Academic Editor: Santanu Saha Ray
Copyright © 2013 Gabriel Magalakwe and Chaudry Masood Khalique. 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.
- M. Wang, Y. Zhou, and Z. Li, “Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics,” Physics Letters A, vol. 216, no. 1–5, pp. 67–75, 1996.
- Y. Chen and Z. Yan, “The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 29, no. 4, pp. 948–964, 2006.
- M. Wang and X. Li, “Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation,” Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1257–1268, 2005.
- M. Wang, X. Li, and J. Zhang, “The(, G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 372, no. 4, pp. 417–423, 2008.
- S. Zhang, “Application of Exp-function method to high-dimensional nonlinear evolution equation,” Chaos, Solitons and Fractals, vol. 38, no. 1, pp. 270–276, 2008.
- H. Zhi and H. Zhang, “Applications of the combined tanh function method with symmetry method to the nonlinear evolution equations,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 385–393, 2007.
- D.-S. Li and H.-Q. Zhang, “A further extended tanh-function method and new soliton-like solutions to the integrable Broer-Kaup (BK) equations in (2 + 1) dimensional spaces,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 537–545, 2004.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
- P. J. Olver, Applications of lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, Berlin, Germany, 2nd edition, 1993.
- N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, vol. 1–3, CRC Press, Boca Raton, Fla, USA, 1994–1996.
- A. M. Wazwaz, “Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method,” Computers and Mathematics with Applications, vol. 50, no. 10–12, pp. 1685–1696, 2005.
- S. Tang and W. Huang, “Bifurcations of travelling wave solutions for the generalized double sinh-Gordon equation,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1774–1781, 2007.
- H. Kheiri and A. Jabbari, “Exact solutions for the double sinh-Gordon and the generalized form of the double sinh-Gordon equations by (/G)-expansion method,” Turkish Journal of Physics, vol. 34, no. 2, pp. 73–82, 2010.
- A.-M. Wazwaz, “Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations,” Chaos, Solitons and Fractals, vol. 28, no. 1, pp. 127–135, 2006.
- K. Parand, J. A. Rad, and A. Rezaei, “Application of Exp-function method for class of nonlinear PDE’s in mathematical physics,” Journal of Applied Mathematics & Informatics, vol. 29, pp. 763–779, 2011.
- A.-M. Wazwaz, “The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations,” Applied Mathematics and Computation, vol. 167, no. 2, pp. 1196–1210, 2005.
- J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 30, no. 3, pp. 700–708, 2006.