Soliton solutions of Hirota equation and Hirota-Maccari system
Abstract
In this paper, the trial equation method is presented to seek the exact solutions of two nonlinear partial differential equations (NLPDEs), namely, the Hirota equation and the Hirota-Maccari system. The obtained solutions are solitary, topological, singular solitons and singular periodic waves. This method is powerful, effective and it can be extended to many NLPDEs.
Keywords
References
- P. Gray and S. Scott, Chemical oscillations and instabilities, Clarendon, Oxford, 1990.
- M. J. Ablowitz and P. A. Clarkson, Soliton, Nonlinear evolution equations and inverse scattering transform, Cambridg University Press, New York,1991.
- V. O. Vakhnenko, E. J. Parkes and A. J. Morrison, A Backlund transformation and the inverse scattering transform method for the generalized Vakhnenko equation, Chaos, Solitons and Fractals, 17 (2003), 683.
- Mahmoud M. El-Borai, Exact solutions for some nonlinear fractional parabolic fractional partial differential equations, Journal of Applied Mathematics and Computation 206 (2008,) 141-153.
- Mahmoud M. El-Borai, Afaf A. Zaghrout and Amal L. Elshaer, Exact solutions for nonlinear partial differential equations by using the extended multiple Riccati equations expansion method, Inter. J. of Research and Reviews in Applied Sciences, 9(3) (2011), 370-381.
- E. M. E. Zayed and A.H. Arnous, DNA dynamics studied using the homogeneous balance method, Chinese Physics Letters, 29(8) (2012), 080203.
- R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, in: R. Bulloygh, P. Coudrey (Eds.), Bäcklund transformation, Springer, Berlin, (1980).
- M. L. Wang, X. Li, Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos Solit. Fract., 24 (2005), 1257-1268.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Authors
M. M. El-borai
*
This is me
Egypt
H. M. El-owaidy
This is me
Egypt
Hamdy M. Ahmed
This is me
Egypt
A. H. Arnous
This is me
Egypt
Publication Date
September 30, 2016
Submission Date
February 17, 2016
Acceptance Date
March 14, 2016
Published in Issue
Year 2016 Volume: 4 Number: 3