利用扩展的(G'/G)展开法求(3 + 1)维YSFY势方程的精确解
Using the Extend (G'/G) Expansion Method to Obtain the Exact Solution of the (3 + 1)-Dimensional Potential YTSF Equation
摘要: 利用扩展的(G'/G)展开法和新的辅助方程,通过借助齐次平衡法确定相关次幂,求解(3 + 1)维Yu-Toda-Sasa-Fukuyama (YTSF)势方程的新精确解,得到了(3 + 1)维YTSF势方程的一些新的精确解的形式,并给出解的相应图形。
Abstract: Using the extend (G'/G)-expansion method and the new auxiliary equations, the new exact solutions of (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation are obtained on the basis of the homogeneous balance method. And some forms of exact solutions of (3 + 1)-dimensional potential (YTSF) equation are given. Furthermore, the corresponding figures are given.
文章引用:莫厚旭, 郭艳凤, 朱萍丽, 廖干杰. 利用扩展的(G'/G)展开法求(3 + 1)维YSFY势方程的精确解[J]. 理论数学, 2019, 9(1): 111-118. https://doi.org/10.12677/PM.2019.91014

参考文献

[1] 王元明. 数学物理方程与特殊函数(第三版) [M]. 北京: 高等教育出版社, 2004.
[2] 傅海明, 戴正德. (2+1)维广义KdV方程的周期孤波解[J]. 平顶山学院学报, 2013, 28(5): 35-38.
[3] 刘建国, 曾志芳. 变系数Sine-Gordon 方程的Bäcklund变换和新的精确解[J]. 系统科学与数学, 2014, 34(6): 763-768.
[4] 傅海明, 戴正德. (2+1)维Nizhnik-Novikov方程的周期孤波解[J]. 江苏师范学报(自然科学版), 2016, 34(2): 33-36.
[5] Kongl, Q. and Dai, C.Q. (2015) Some Discussions about Variable Separation of Nonlinear Models Using Riccati Equation Expansion Method. Nonlinear Dynamics, 81, 1553-1561.
[Google Scholar] [CrossRef
[6] Yu, S.J., Toda, K., Sasa, N. and Fukuyama, T. (1998) N-Solitions to the Bo-goyavlenskii-Schiff Equation and Aquest for the Solition in (3+1)-Dimensions. Journal of Physics A, 31, 3337.
[Google Scholar] [CrossRef
[7] Schff, J. and Painleve, T. (1992) Their Asymptotics and Physical Applica-tions. Plenum, New York.
[8] Vladimirov, V.A. and Maczka, C. (2007) Exact Solutions of Generalized Burgers Equation, De-scribing Travelling Fronts and Their Interaction. Reports on Mathematical Physics, 60, 317-328.
[Google Scholar] [CrossRef
[9] Darvishi, M.T., Najafi, M., Kavitha, L. and Venkatesh, M. (2012) Stair and Step Solition Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations. Communications in Theoretical Physics, 58, 785-794.
[Google Scholar] [CrossRef
[10] Tan, W. and Dai, Z.D. (2016) Dynamics of Kinky Wave for (3+1)- Dimensional Potential Yu-Toda-Sasa-Fukuyama. Nonlinear Dynamics, 85, 817-823.
[Google Scholar] [CrossRef
[11] Yun, Z. (2003) New Families of Nontravelling Wave Solutions to a New (3+1)-Dimensional Potential-YTSF Equation. Physics Letters A, 318, 78-83.
[Google Scholar] [CrossRef
[12] Zhang, T., Xuan, H.N., Zhang, D.F. and Wang, C.J. (2007) Nontraveling Wave Solutions to a (3+1) Dimensional Potential YTSF Equation and a Simplified Model for Reacting Mixtures. Chaos, Solitions Fractals, 34, 1006-1013.
[Google Scholar] [CrossRef
[13] Hasibun, N. and Farah, A. (2014) New Generalized and Improved (G'/G)-Expansion Method for Nonlinear Evolution Equations in Mathematical Physic. Journal of the Egyptian Mathematical Society, 22, 390-395.
[Google Scholar] [CrossRef