Application of the improved F-expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations |
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Authors: | Md Shafiqul Islam Kamruzzaman Khan M Ali Akbar |
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Institution: | 1. Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh;2. Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh |
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Abstract: | In this article, we pay attention to the analytical method named, the improved F-expansion method combined with Riccati equation for finding the exact traveling wave solutions of the Benney–Luke equation and the Phi-4 equation. By means of this method we have explored three classes of explicit solutions-hyperbolic, trigonometric and rational solutions with some free parameters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. Our outcomes disclose that this method is very active and forthright way of formulating the exact solutions of nonlinear evolution equations arising in mathematical physics and engineering. |
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Keywords: | Benney–Luke equation Phi-4 equation Exact solution NLEEs 02 30 Jr 02 70 Wz 05 45 Yv 94 05 Fg 35K99 35P05 35P99 |
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