Abstract
In this paper, the exact solutions for (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation have been investigated. By Lie group method and traveling wave transformation, we obtain two symmetry reduced equations of (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation. Then three classes of non-traveling wave exact solutions of (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation are constructed. At last, we achieve some computer simulations to illustrate our main results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
He, J.H., Wu, X.H.: Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30(3), 700–708 (2006)
He, J.H., Abdou, M.A.: New periodic solutions for nonlinear evolution equations using exp-function method. Chaos Solitons Fractals 34(5), 1421–1429 (2007)
Abdou, M.A.: The extended F-expansion method and its application for a class of nonlinear evolution equations. Chaos Solitons Fractals 31(1), 95–104 (2007)
Malfliet, W., Hereman, W.: The tanh method, I: exact solutions of nonlinear evolution and wave equations. Phys. Scr. 54, 563–568 (1996)
Taghizadeh, N., Neirameh, A.: New complex solutions for some special nonlinear partial differential systems. Comput. Math. Appl. 62(4), 2037–2044 (2011)
Eslami, M., Mirzazadeh, M.A., Neirameh, A.: New exact wave solutions for Hirota equation. Pramana J. Phys. 84(1), 3–8 (2015)
Wazwaz, A.M.: A sine-cosine method for handling nonlinear wave equations. Math. Comput. Model 40, 499–508 (2004)
Ma, W.X., Lee, J.H.: A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation. Chaos Solitons Fractals 42(3), 1356–1363 (2009)
Ablowitz, M.J., Clarkson, P.A.: Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform. Cambrige University Press, Cambridge (1991)
Li, B., Chen, Y., Zhang, H.: Auto-Bäcklund transformation and exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order. Phys. Setters A 305(6), 377–382 (2002)
Gu, C.H., Guo, B.L., Li, Y.K.: Soliton Theory and its Applications. Zhejiang Science and Technology Press, Zhejiang (1990). (in Chinese)
Zhao, Z.H., He, X.Y., Han, S.: Symmetry reduction and explicit non-traveling wave solutions of (3+1)-dimensional YTSF equation. J. Northwest Norm. Univ. (Nat. Sci.) 48(6), 36–43 (2012). (in Chinese)
Tian, C.: Lie Group and its Applications in Partial Differential Equations. Higher Education Press, Beijing (2001). (in Chinese)
Yu, S., Toda, K., Sasa, N., Fukuyama, T.: N soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3+1) dimensions. J. Phys. A Gener. Phys. 31(14), 3337–3347 (1998)
Lang, S.: Elliptic Functions, 2nd edn. Springer, New York (1987)
Conte, R., Musette, M.: Elliptic general analytic solutions. Stud. Appl. Math. 123(1), 63–81 (2009)
Yuan, W.J., Li, Y.Z., Lin, J.M.: Meromorphic solutions of an auxiliary ordinary differential equation using complex method. Math. Methods Appl. Sci. 36(13), 1776–1782 (2013)
Acknowledgements
This work was completed with the support of the NSF of China (No.11271090) and NSFs of Guangdong Province (No. 2016A030310257 and 2015A030313346). This work was supported by the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University when the authors worked as visiting scholars. The authors would like to express their hearty thanks to Chern Institute of Mathematics provided very comfortable research environments to them.
Recommender: Yadong Shang, Guangzhou University, Professor.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Aminakbari, N., Dang, Gq., Gu, Yy., Yuan, Wj. (2018). Non-traveling Wave Exact Solutions of (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation. In: Cao, BY. (eds) Fuzzy Information and Engineering and Decision. IWDS 2016. Advances in Intelligent Systems and Computing, vol 646. Springer, Cham. https://doi.org/10.1007/978-3-319-66514-6_37
Download citation
DOI: https://doi.org/10.1007/978-3-319-66514-6_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66513-9
Online ISBN: 978-3-319-66514-6
eBook Packages: EngineeringEngineering (R0)