有理函数变换法求解两类扩展的(3 + 1)维Jimbo-Miwa方程
The Transformed Rational Method for Solving Two Extended (3 + 1)-Dimensional Jimbo-Miwa Equations
摘要: 在本文中，我们引入有理函数变换法对两类扩展的(3 + 1)维Jimbo-Miwa方程进行了研究。通过这种方法并借助于Maple软件得到了它们新的行波精确解，而且如果我们选择不同的常微分方程，还可以得到不同类的行波解，补充了以往文献的研究成果。
Abstract: In this paper, two extended (3 + 1)-dimensional Jimbo-Miwa equations can be researched with the transformed rational function method. As a result, new exact travelling wave solutions for two extended (3 + 1)-dimensional Jimbo-Miwa equations are obtained by means of Maple software. What’s more, if we choose different ordinary differential equations, we can obtain different types of travelling wave solutions which supplement the existing literatures.
文章引用：哈金婷, 关雪, 张辉群. 有理函数变换法求解两类扩展的(3 + 1)维Jimbo-Miwa方程[J]. 应用数学进展, 2018, 7(10): 1247-1255. https://doi.org/10.12677/AAM.2018.710145

参考文献

[1] Wang, M.L. (1995) Solitary Wave Solutions for Variant Boussinesq Equations. Physics Letters A, 199, 169-172. [Google Scholar] [CrossRef] 
[2] Wang, M.L. (1996) Exact Solutions for a Compound KdV-Burgers Equation. Physics Letters A, 213, 279-287. [Google Scholar] [CrossRef] 
[3] Bluman, G.W. and Kumei, S. (1989) Symmetries and Differential Equations. Springer-Verlag, Berlin. [Google Scholar] [CrossRef] 
[4] Cantwell, B.J. (2002) Introduction to Symmetry Analysis. Cambridge University Press, Cambridge.
[5] Dong, H.H., et al. (2016) A New Integrable Symplectic Map and the Lie Point Symmetry Associated with Nonlinear Lattice Equations. Journal of Nonlinear Sciences and Applications, 9, 5107-5118. [Google Scholar] [CrossRef] 
[6] Zhou, Y.B., Wang, M.L. and Wang, Y.M. (2003) Periodic Wave Solutions to a Coupled KdV Equations with Variable Coefficients. Physics Letters A, 208, 31-36. [Google Scholar] [CrossRef] 
[7] Liu, S.K., et al. (2001) Jacobi Elliptic Function Expansion Method and Periodic Wave Solutions of Nonlinear Wave Equations. Physics Letters A, 289, 69-74. [Google Scholar] [CrossRef] 
[8] He, J.H. and Wu, H.X. (2006) Exp-Function Method for Nonlinear Wave Equations. Chaos Solitons Fractals, 30, 700-708. [Google Scholar] [CrossRef] 
[9] He, J.H. and Abdou, M.A. (2007) New Periodic Solutions for Nonlinear Evolution Equations Using Exp-Function Method. Chaos Solitons Fractals, 34, 1421-1429. [Google Scholar] [CrossRef] 
[10] Ablowitz, M.J. and Segur, H. (1981) Solitons and the Inverse Scattering Transform. SIMA, Philadephia. [Google Scholar] [CrossRef] 
[11] Novikov, S.P., Manakov, S.V., Pitaevskii, L.P. and Zakharov, V.E. (1984) Theory of Solitons: The Inverse Scattering Method. Springer-Verlag, Berlin.
[12] Ma, W.X. and Lee, J.H. (2009) A Transformed Rational Function Method and Exact Solutions to the (3 + 1)-Dimensional Jimbo-Miwa Equation. Chaos Solitons Fractals, 42, 1356-1363. [Google Scholar] [CrossRef] 
[13] Jimbo, M. and Miwa, T. (1983) Solitons and Infnite Dimensional Lie Algebras. Publications of Research Institute for Mathematical Sciences, 19, 943-1001. [Google Scholar] [CrossRef] 
[14] Zhang, H.Q. and Ma, W.X. (2014) Extended Transformed Rational Function Method and Applications to Complexiton Solutions. Applied Mathematics Computation, 230, 509-515. [Google Scholar] [CrossRef] 
[15] Hong, W.P. and Oh, K.S. (2000) New Solitonic Solutions to a (3 + 1)-Dimensional Jimbo-Miwa Equation. Computers & Mathematics with Applications, 39, 29-31. [Google Scholar] [CrossRef] 
[16] Wazwaz, A.M. (2008) Multiple-Soliton Solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF Equations. Applied Mathematics Computation, 203, 592-597. [Google Scholar] [CrossRef] 
[17] Yang, J.Y. and Ma, W.X. (2017) Abundant Lump-Type Solutions of the Jimbo-Miwa Equation in (3 + 1)-Dimensions. Computers & Mathematics with Applications, 73, 220-225. [Google Scholar] [CrossRef] 
[18] Zhang, L., Lin, Y.Z. and Liu, Y.P. (2014) New Solitary Wave Solutions for Two Nonlinear Evolution Equations. Computers & Mathematics with Applications, 67, 1595-1606. [Google Scholar] [CrossRef] 
[19] Singh, M. and Gupta, R.K. (2016) Bäcklund Transformations, Lax System, Conservation Laws and Multisoliton Solutions for Jimbo-Miwa Equation with Bell-Polynomials. Communications in Nonlinear Science and Numerical Simulation, 37, 362-373. [Google Scholar] [CrossRef] 
[20] Wazwaz, A.M. (2017) Multiple-Soliton Solutions for Extended (3 + 1)-Dimensional Jimbo Miwa Equations. Applied Mathematics Letters, 64, 21-26. [Google Scholar] [CrossRef] 
[21] Sun, H.Q. and Chen, A.H. (2017) Lump and Lump-Kink Solutions of the (3 + 1)-Dimensional Jimbo-Miwa and Two Extended Jimbo-Miwa Equations. Applied Mathematics Letters, 68, 55-61. [Google Scholar] [CrossRef] 
[22] Li Y.Z. and Liu, J.G. (2018) Abundant Lump and Lump-Kink Solutions for the Extended (3 + 1)-Dimensional Jimbo-Miwa Equation. Nonlinear Dynamics, 91, 497-504. [Google Scholar] [CrossRef] 
[23] Li, H. and Li, Y.Z. (2018) Meromorphic Exact Solutions of Two Extended (3 + 1)-Dimensional Jimbo-Miwa Equations. Applied Mathematics Computation, 333, 369-375. [Google Scholar] [CrossRef] 
[24] Zhang, H.Q. and Ma, W.X. (2014) Extended Transformed Rational Function Method and Applications to Complexiton Solutions. Applied Mathematics and Computation, 230, 509-515. [Google Scholar] [CrossRef] 

为你推荐