On Exact Solutions of Phi-4 Partial Differential Equation Using the Enhanced Modified Simple Equation Method
DOI:
https://doi.org/10.24203/ajas.v6i4.5433Keywords:
Nonlinear differential equation, exact solutions, enhanced modified simple equation method, Phi-4 equation.Abstract
Constructing exact solutions of nonlinear ordinary and partial differential equations is an important topic in various disciplines such as Mathematics, Physics, Engineering, Biology, Astronomy, Chemistry,… since many problems and experiments can be modeled using these equations. Various methods are available in the literature to obtain explicit exact solutions. In this correspondence, the enhanced modified simple equation method (EMSEM) is applied to the Phi-4 partial differential equation. New exact solutions are obtained.References
J. H. He and X. H. Wu, “Exp-function method for nonlinear wave equations,†Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700-708, 2006.
M. A. Akbar, N. H. M. Ali, “New Solitary and Periodic Solutions of Nonlinear Evolution Equation by Exp-Function Method,†World Appl. Sci. J., 17 (12), pp. 1603-1610, 2012.
M. A. Abdou, “The extended Tanh method and its applications for solving nonlinear physical models,†Applied Mathematics and Computation, vol. 190, no. 1, pp. 988-996, 2007.
E. Fan, “Extended tanh-function method and its applications to nonlinear equations,†Physics Letters A, vol. 277, no. 4-5, pp. 212-218, 2000.
M. L. Wang, “Solitary wave solutions for variant Boussinesq equations,†Physics Letters A, vol. 199, no. 3-4, pp. 169-172, 1995.
E. M. E. Zayed, H. A. Zedan, and K. A. Gepreel, “On the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV of equations,†Chaos, Solitons & Fractals, vol. 22, no. 2, pp. 285-303,2004.
M. Wang, X. Li, and J. Zhang, “The (G’/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, †Physics Letters A, vol. 372, no. 4, pp. 417-423, 2008.
E. M. E. Zayed and K. A. Gepreel, “ The (G’/G)-expansion method for finding the traveling wave solutions of nonlinear partial differential equations in mathematical physics,†Journal Math. Phys., 50 (2009) 013502-013514.
M. R. Miura, Backlund Transformation, Springer, Berlin, Germany, 1978.
D. Lu and Q. Shi, “New Jacobi elliptic functions solutions for the combined KdV-MKdV equation,†International Journal of Nonlinear science, vol. 10, no. 3, pp. 320-325, 2010.
J. Akter, M. A. Akbar, “Exact solutions to the Benny-Luke equation and the Phi-4 equation by using the modified simple equation methodâ€, Results in Physics, 5, pp. 125-130, 2015.
E. M. E. Zayed and S. A. H. Ibrahim, “Exact solutions of nonlinear evolution equations in mathematical physics using the modified simple equation method,†Chinese Physics Letters, vol. 29, no. 6, Article ID 060201, 2012.
C. Zhang and Z. Zhang, “Application of the enhanced modified simple equation method for Burger-Fisher and modified Volterra equations,†Advances in Difference Equations, 2017.
Downloads
Published
How to Cite
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.