On Exact Solutions of Phi-4 Partial Differential Equation Using the Enhanced Modified Simple Equation Method
Keywords:Nonlinear differential equation, exact solutions, enhanced modified simple equation method, Phi-4 equation.
AbstractConstructing exact solutions of nonlinear ordinary and partial differential equations is an important topic in various disciplines such as Mathematics, Physics, Engineering, Biology, Astronomy, Chemistry,â€¦ 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.
J. H. He and X. H. Wu, â€œExp-function method for nonlinear wave equations,â€ Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700-708, 2006.
M. A. Akbar, N. H. M. Ali, â€œNew Solitary and Periodic Solutions of Nonlinear Evolution Equation by Exp-Function Method,â€ World Appl. Sci. J., 17 (12), pp. 1603-1610, 2012.
M. A. Abdou, â€œThe extended Tanh method and its applications for solving nonlinear physical models,â€ Applied Mathematics and Computation, vol. 190, no. 1, pp. 988-996, 2007.
E. Fan, â€œExtended tanh-function method and its applications to nonlinear equations,â€ Physics Letters A, vol. 277, no. 4-5, pp. 212-218, 2000.
M. L. Wang, â€œSolitary wave solutions for variant Boussinesq equations,â€ Physics Letters A, vol. 199, no. 3-4, pp. 169-172, 1995.
E. M. E. Zayed, H. A. Zedan, and K. A. Gepreel, â€œOn the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV of equations,â€ Chaos, Solitons & Fractals, vol. 22, no. 2, pp. 285-303,2004.
M. Wang, X. Li, and J. Zhang, â€œThe (Gâ€™/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, â€ Physics Letters A, vol. 372, no. 4, pp. 417-423, 2008.
E. M. E. Zayed and K. A. Gepreel, â€œ The (Gâ€™/G)-expansion method for finding the traveling wave solutions of nonlinear partial differential equations in mathematical physics,â€ Journal Math. Phys., 50 (2009) 013502-013514.
M. R. Miura, Backlund Transformation, Springer, Berlin, Germany, 1978.
D. Lu and Q. Shi, â€œNew Jacobi elliptic functions solutions for the combined KdV-MKdV equation,â€ International Journal of Nonlinear science, vol. 10, no. 3, pp. 320-325, 2010.
J. Akter, M. A. Akbar, â€œExact 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, â€œExact solutions of nonlinear evolution equations in mathematical physics using the modified simple equation method,â€ Chinese Physics Letters, vol. 29, no. 6, Article ID 060201, 2012.
C. Zhang and Z. Zhang, â€œApplication of the enhanced modified simple equation method for Burger-Fisher and modified Volterra equations,â€ Advances in Difference Equations, 2017.
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