扩展的φ´/φ展开法及Sharma-Tasso-Olver方程的行波解
Generalized φ´/φExpansion Method and the Traveling Wave Solutions of the STO Equation
摘要: 本文在原有扩展的φ´/φ展开法基础之上，不考虑&phi满足的辅助方程，只利用方程本身来确定，进而确定方程的解。文章讨论求解了Sharma-Tasso-Olver(STO)方程，获得了STO方程的行波解和三角函数解。
Abstract: This paper is about to discuss the method which is based on the generalized φ´/φ -expansion method, and explain how to determine &phi by the equation itself without considering the auxiliary equation to make sure the solutions of the equation. This paper discusses the Sharma-Tasso-Olver (STO) equation and obtains the traveling wave solutions and trigonometric function solutions of the STO equation.
文章引用：韩园媛, 李德生, 黄婷. 扩展的φ´/φ展开法及Sharma-Tasso-Olver方程的行波解[J]. 理论数学, 2013, 3(3): 188-194. http://dx.doi.org/10.12677/PM.2013.33028

参考文献

[1] Y. S. Li, W. X. Ma and J. E. Zhang. Darboux transformation of classical Boussinesq system and its new solutions. Physics Letters A, 2000, 275 (1): 60-66.
[2] 屠规彰. Boussinesq方程的Bäcklund变换与守恒律[J]. 应用数学学报, 1981, 4(1): 63-68.
[3] E. G. Fan. Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations. Physic Letters A, 2002, 294(1): 26-30.
[4] H. A. Zedan. Exact solutions for the generalized KdV equation by using Bäcklund transformations. Journal of the Franklin Institute, 2011, 348 (8): 1751-1768.
[5] 套格图桑, 斯仁道尔吉. 辅助方程构造(2 + 1)维Hybrid-Lattice系统和离散的mKdV方程的精确解[J]. 物理学报, 2002, 56(2): 627-636.
[6] H. W. Tam, W. X. Ma, X. B. Hu, et al. The hirota-satsuma coupled KdV equation and a coupled Ito system revisited. Journal of the Physical Society of Japan, 2000, 69(1): 45-52.
[7] C. Z. Qu. Allowed transformation and symmetry classes of variable coefficient Burgers equation. IMA Journal of Applied Mathematics, 1995, 54(3): 203-225.
[8] M. L. Wang, X. Z. Li and J. L. Zhang. The -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 2008, 372: 417-423.
[9] S. Zhang, J.-L. Tong and W. Wang. A generalized -expansion method for the mKdV equation with variable coefficients. Physics Letters A, 2008, 372: 2254-2257.
[10] J. Zhang, X. L. Wei and Y. J. Lu. A generalized -expansion method and its applications. Physics Letters A, 2008, 372: 3653-3658.
[11] S. Zhang, W. Wang and J.-L. Tong. A generalized -expansion method and its application to the (2 + 1)-dimensional Broer-Kaup equations. Applied Mathematics and Computation, 2009, 209: 399-404.
[12] K. A. Gepreel. A generalized -expansion method to find the traveling wave solutions of nonlinear evolution equations. Journal of Partial Differential Equations, 2011, 24(1): 55-69.
[13] B. Tang, Y. N. Wei and S. L. Wang. Variable-coefficient discrete -expansion method for nonlinear differential-difference equations. Physics Letters A, 2011, 375: 3355-3361.
[14] A. Bansal, R. K.Gupta. Modified -expansion method for finding exact wave solutions of the coupled Klein-Gordon-Schrödinger equation. Mathematical Methods in the Applied Sciences, 2012, 35(10): 1175-1187.
[15] X. H. Liu, W. G. Zhang and Z. M. Li. Application of Improved -Expansion Method for the Complex KDV Equation. Advanced Science Letters, 2012, 7: 586-588.
[16] J. C. Chen, B. Li. Multiple -expansion method and its applications to nonlinear evolution equations in mathematical physics. Pramana- Journal of Physics, 2012, 78(3): 375-388.

为你推荐