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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 534017, 6 pages
Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation
1College of Sciences, China University of Mining and Technology, Xuzhou 221116, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China
Received 19 December 2013; Revised 5 January 2014; Accepted 6 January 2014; Published 26 February 2014
Academic Editor: Chaudry Masood Khalique
Copyright © 2014 Zhonglong Zhao 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.
- E. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters A, vol. 277, no. 4-5, pp. 212–218, 2000.
- M. L. Wang, “Exact solutions for a compound KdV-Burgers equation,” Physics Letters A, vol. 213, no. 5-6, pp. 279–287, 1996.
- G. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1989.
- W.-X. Ma, C.-X. Li, and J. He, “A second Wronskian formulation of the Boussinesq equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 12, pp. 4245–4258, 2009.
- Y. Zhang, T.-F. Cheng, D.-J. Ding, and X.-L. Dang, “Wronskian and Grammian solutions for -dimensional soliton equation,” Communications in Theoretical Physics, vol. 55, no. 1, pp. 20–24, 2011.
- V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin, Germany, 1991.
- R. Hirota, “Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons,” Physical Review Letters, vol. 27, no. 18, pp. 1192–1194, 1971.
- R. Hirota and J. Satsuma, “-soliton solutions of model equations for shallow water waves,” Journal of the Physical Society of Japan, vol. 40, no. 2, pp. 611–612, 1976.
- X.-B. Hu and W.-X. Ma, “Application of Hirota's bilinear formalism to the Toeplitz lattice—some special soliton-like solutions,” Physics Letters A, vol. 293, no. 3-4, pp. 161–165, 2002.
- X.-B. Hu and W.-M. Xue, “A bilinear Bäcklund transformation and nonlinear superposition formula for the negative Volterra hierarchy,” Journal of the Physical Society of Japan, vol. 72, no. 12, pp. 3075–3078, 2003.
- S. P. Novikov, “The periodic problem for the Korteweg-de Vries equation,” Functional Analysis and Its Applications, vol. 8, no. 3, pp. 236–246, 1974.
- A. Nakamura, “A direct method of calculating periodic wave solutions to nonlinear evolution equations. I. Exact two-periodic wave solution,” Journal of the Physical Society of Japan, vol. 47, no. 5, pp. 1701–1705, 1979.
- A. Nakamura, “A direct method of calculating periodic wave solutions to nonlinear evolution equations. II. Exact one-periodic and two-periodic wave solution of the coupled bilinear equations,” Journal of the Physical Society of Japan, vol. 48, no. 4, pp. 1365–1370, 1980.
- Y. C. Hon, E. Fan, and Z. Qin, “A kind of explicit quasi-periodic solution and its limit for the Toda lattice equation,” Modern Physics Letters B, vol. 22, no. 8, pp. 547–553, 2008.
- E. Fan and K. W. Chow, “On the periodic solutions for both nonlinear differential and difference equations: a unified approach,” Physics Letters A, vol. 374, no. 35, pp. 3629–3634, 2010.
- E. Fan, “Supersymmetric KdV-Sawada-Kotera-Ramani equation and its quasi-periodic wave solutions,” Physics Letters A, vol. 374, no. 5, pp. 744–749, 2010.
- W.-X. Ma, R. Zhou, and L. Gao, “Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in dimensions,” Modern Physics Letters A, vol. 24, no. 21, pp. 1677–1688, 2009.
- S.-F. Tian and H.-Q. Zhang, “Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations,” Journal of Mathematical Analysis and Applications, vol. 371, no. 2, pp. 585–608, 2010.
- S.-F. Tian and H.-Q. Zhang, “Riemann theta functions periodic wave solutions and rational characteristics for the -dimensional and -dimensional Ito equation,” Chaos, Solitons & Fractals, vol. 47, pp. 27–41, 2013.
- C.-W. Cao and X. Yang, “Algebraic-geometric solution to -dimensional Sawada-Kotera equation,” Communications in Theoretical Physics, vol. 49, no. 1, pp. 31–36, 2008.
- A.-M. Wazwaz, “Multiple soliton solutions for -dimensional Sawada-Kotera and Caudrey-Dodd-Gibbon equations,” Mathematical Methods in the Applied Sciences, vol. 34, no. 13, pp. 1580–1586, 2011.
- V. G. Dubrovsky and Y. V. Lisitsyn, “The construction of exact solutions of two-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations via -dressing method,” Physics Letters A, vol. 295, no. 4, pp. 198–207, 2002.
- R. A. Zait, “Bäcklund transformations, cnoidal wave and travelling wave solutions of the SK and KK equations,” Chaos, Solitons & Fractals, vol. 15, no. 4, pp. 673–678, 2003.
- R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, UK, 2004.
- X. Lü, T. Geng, C. Zhang, H.-W. Zhu, X.-H. Meng, and B. Tian, “Multi-soliton solutions and their interactions for the -dimensional Sawada-Kotera model with truncated Painlevé expansion, Hirota bilinear method and symbolic computation,” International Journal of Modern Physics B, vol. 23, no. 25, pp. 5003–5015, 2009.
- X. Lü, B. Tian, K. Sun, and P. Wang, “Bell-polynomial manipulations on the Bäcklund transformations and Lax pairs for some soliton equations with one Tau-function,” Journal of Mathematical Physics, vol. 51, no. 11, Article ID 113506, 2010.