利用exp(-G(ξ))方法和拟设函数法求Sharma-Tasso-Olver方程精确解
The Exact Solutions of the Sharma-Tasso-Olver Equation Using exp(-G(ξ)) Method and Ansatz Method
DOI: 10.12677/AAM.2019.82025, PDF,  被引量   
作者: 张逢燕, 王俊梅：山东师范大学，数学与统计学院，山东 济南；李冬雪：德州市第十中学，山东 德州
关键词: Sharma-Tasso-Olver方程；exp(-G(ξ))方法；孤子解；拟设双曲函数法；Sharma-Tasso-Olver Equation； exp(-G(ξ))-Method； Soliton Solution； Ansatz Method
摘要: 本文运用行波变换和齐次平衡原理对Sharma-Tasso-Olver方程进行化简，得到约化的常微分方程。利用exp(-G(ξ))方法和拟设双曲函数法求得方程的三角函数解、双曲函数解、有理函数解和孤子解。
Abstract: Using the traveling wave transformation and homogeneous balance simplified the Shar-ma-Tasso-Olver equation to obtain the reduced ordinary differential equations, using the exp(-G(ξ))-method to get the trigonometric function solution, hyperbolic function solution and the rational function solution. In addition, an exact soliton solution is provided by using the Ansatz method.
文章引用：张逢燕, 李冬雪, 王俊梅. 利用exp(-G(ξ))方法和拟设函数法求Sharma-Tasso-Olver方程精确解[J]. 应用数学进展, 2019, 8(2): 219-226. https://doi.org/10.12677/AAM.2019.82025

参考文献

[1] Shang, Y.D., Huang, Y. and Yuan, W.J. (2011) Bäcklund Transformations and Abundant Exact Explicit Solutions of the Sharma-Tasso-Olver Equation. Applied Mathematics and Computation, 217, 7172-7183. [Google Scholar] [CrossRef] 
[2] Fan, E.G. and Zhang, H.Q. (1998) A New Approach to Bäcklund Transformations of Nonlinear Evolution Equations. Applied Mathematics and Mechanics, 19, 645-650.
[3] Shang, Y. (2008) The Extended Hyperbolic Functions Method and Exact Solutions to the Long-Short Wave Resonance Equations. Chaos, Solitons & Fractals, 36, 762-771. [Google Scholar] [CrossRef] 
[4] Wang, S., Tang, X.Y. and Lou, S.Y. (2004) Soliton Fission and Fusion: Burgers Equation and Sharma-Tasso-Olver Equation. Chaos, Solitons & Fractals, 21, 231-239. [Google Scholar] [CrossRef] 
[5] Yan, Z.Y. (2003) Integrability of Two Types of the (2 + 1)-Dimensional Generalized Sharma-Tasso-Olver Integro-Differential Equations. Acta Mathematica Scientia, 22, 302-324.
[6] Shang, Y.D., Qin, J.H. and Huang, Y. (2008) Abundant Exact and Explicit Solitary Wave and Periodic Wave Solutions to the Sharma-Tasso-Olver Equation. Applied Mathematics and Computation, 202, 532-538. [Google Scholar] [CrossRef] 
[7] Kudryashov, N.A. and Loguinova, N.B. (2008) Extended Simplest Equation Method for Nonlinear Differential Equations. Applied Mathematics and Computation, 205, 396-402.
[8] Bekir, A. and Boz, A. (2008) Exact Solutions for Nonlinear Evolution Equations Using Exp-Function Method. Physics Letters A, 372, 1619-1625. [Google Scholar] [CrossRef] 
[9] Erbas, B. and Yusufoglu, E. (2009) Exp-Function Method for Constructing Exact Solutions of Sharma-Tasso-Olver Equation. Chaos, Solitons & Fractals, 41, 2326-2330. [Google Scholar] [CrossRef] 
[10] Lian, Z.J. and Lou, S.Y. (2005) Symmetries and Exact Solutions of the Sharma-Tasso-Olver Equation. Nonlinear Anal, 63, e1167-e1177.
[11] Inan, I.E. and Kaya, D. (2007) Exact Solutions of Some Nonlinear Partial Differential Equations. Physica A, 381, 104-115. [Google Scholar] [CrossRef] 
[12] Wazwaz, A.M. (2007) New Solitons and Kinks Solutions to the Sharma-Tasso-Olver Equation. Applied Mathematics and Computation, 188, 1205-1213. [Google Scholar] [CrossRef] 
[13] Akbulut, A., Kaplan, M. and Tascan, F. (2017) The Investigation of Exact Solutions of Nonlinear Partial Differential Equations by Using Method. Optik, 132, 382-387. [Google Scholar] [CrossRef] 
[14] Roshid, H.O., Alam, M.N. and Akbar, M.A. (2015) Exact Trav-eling Wave Solutions to the (3+1)-Dimensional mKdV –ZK and the (2+1)-Dimensional Burgers Equations via -Expansion Method. Alexandria Engineering Journal, 54, 635-644. [Google Scholar] [CrossRef] 
[15] Bhrawy, A.H. and Obaid, M. (2012) New Exact Solutions for the Zhiber-Shabat Equation Using the Extended F-Expansion Method. Life Sciences, 9, 1154-1162.
[16] Fan, E.G. (2000) Two New Applications of the Homogeneous Balance Method. Physics Letters A, 265, 353-357. [Google Scholar] [CrossRef] 
[17] Zhang, H.Q. (2001) Extension and Application of Homogenous Balance Method. Applied Mathematics and Mechanics, 21, 321-325.
[18] Jawad, A.J.M., Petkovic, M.D. and Biswas, A. (2010) Soliton Solutions of Burgers Equations and Perturbed Burgers Equation. Applied Mathematics and Computation, 216, 3370-3377. [Google Scholar] [CrossRef] 
[19] Wang, G.W. and Kara, A.H. (2018) Group Analysis, Fractional Explicit Solutions and Conservation Laws of Time Fractional Generalized Burgers Equation. Communications in Theoretical Physics, 69, 5-8.

为你推荐