Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31584
Some Complexiton Type Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation

Authors: Mohammad Taghi Darvishi, Mohammad Najafi


By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

Keywords: Jimbo-Miwa equation, painleve analysis, Hirota's bilinear form, computerized symbolic computation.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1575


[1] X.Y. Tang, Z.F. Liang, Variable separation solutions for the (3+1)- dimensional Jimbo-Miwa equation, Phys. Lett. A, 351 (2006) 398-402.
[2] G.-Q. Xu, The soliton solutions, dromions of the Kadomtsev-Petviashvili and Jimbo-Miwa equations in (3+1)-dimensions, Chaos, Solitons and Fractals, 30 (2006) 71-76.
[3] Z.D. Dai, Z. Li, Z.J. Liu, D.L. Li, Exact cross kink-wave solutions and resonance for the Jimbo-Miwa equation, Physica A, 384 (2007) 285-290.
[4] D. Wang, W. Sun, C. Kong, H.Q. Zhang, New extended rational expansion method and exact solutions of Boussinesq equation and Jimbo-Miwa equations, Appl. Math. Comput., 189 (2007) 878-886.
[5] Z.D. Dai, J. Liu, X.P. Zeng, Z.J. Liu, Periodic kink-wave and kinky periodic-wave solutions for the Jimbo-Miwa equation, Phys. Lett. A, 372 (2008) 5984-5986.
[6] T. Ozis, I. Aslan, Exact and explicit solutions to the (3+1)-dimensional Jimbo-Miwa equation via the Exp-function method, Phys. Lett. A, 372 (2008) 7011-7015.
[7] A.M. Wazwaz, Multiple-soliton solutions for the Calogero- Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations, Appl. Math. Comput., 203 (2008) 592-597.
[8] W.-X. Ma, J.-H. Lee, A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation, Chaos, Solitons and Fractals, 42 (2009) 1356-1363.
[9] S.-H. Ma, J.-P. Fang, C.-L. Zheng, New exact solutions for the (3+1)- dimensional Jimbo-Miwa system, Chaos, Solitons and Fractals, 40 (2009) 1352-1355.
[10] M. Song, Y. Geb, Application of the (G G )-expansion method to (3+1)- dimensional nonlinear evolution equations, Comput. Math. Appl., 60 (2010) 1220-1227.
[11] Z. Li, Z.D. Dai, J. Liu, Exact three-wave solutions for the (3+1)- dimensional Jimbo-Miwa equation, Comput. Math. Appl., (in press), doi:10.1016/j.camwa.2010.08.070.
[12] Z. Li, Z.D. Dai, Abundant new exact solutions for the (3+1)-dimensional Jimbo-Miwa equation, J. Math. Anal. Appl., 361 (2010) 587-590.
[13] N.A. Kudryashov, D. I. Sinelshchikov, A note on "Abundant new exact solutions for the (3+1)-dimensional imbo-Miwa equation", J. Math. Anal. Appl., 371 (2010) 393-396.
[14] W. Hong, K.S. Oh, New solitonic solutions to a (3+1)-dimensional Jimbo-Miwa equation, Comput. Math. Appl., 39(5-6) (2000) 29-31.
[15] D.L. Wang, H.W. Tam, W.M. Xue, Soliton solutions to the Jimbo-Miwa equations and the Fordy-Gibbons-Jimbo-Miwa equation, Phys. Lett. A, 262(4-5) (1999) 310-320.
[16] B. Tian, Y.T. Gao, H. Woopyo, The solitonic features of a non integrable (3+1)-dimensional Jimbo-Miwa equation, Comput. Math. Appl., 44(3-4) (2002) 525-528.
[17] Z. Zhao, Z.D. Dai, S. Han, The EHTA for nonlinear evolution equations, Appl. Math. Comput., (in press), doi:10.1016/j.amc.2010.09.069.