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New solitary wave solutions and stability analysis of the Benney-Luke and the Phi-4 equations in mathematical physics

1 Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran
2 Firat University, Science Faculty, Department of Mathematics, 23119 Elazig, Turkey
3 Federal University Dutse, Science Faculty, Department of Mathematics, 7156 Dutse, Nigeria
4 Cankaya University, Science Faculty, Department of Mathematics, 06530 Ankara, Turkey
5 Institute of Space Sciences, Magurele, Romania

Special Issues: Recent Advances in Fractional Calculus with Real World Applications

In this paper, we present new solitary wave solutions for the Benney-Luke equation (BLE) and Phi-4 equation (PE). The new generalized rational function method (GERFM) is used to reach such solutions. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. It is proved that, both the governing equations are stable. We can also solve other nonlinear system of PDEs which are involve in mathematical physics and many other branches of physical sciences with the help of this new method.
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Keywords Benney-Luke equation; Phi-4 equation; GERFM; stability analysis

Citation: Behzad Ghanbari, Mustafa Inc, Abdullahi Yusuf, Dumitru Baleanu. New solitary wave solutions and stability analysis of the Benney-Luke and the Phi-4 equations in mathematical physics. AIMS Mathematics, 2019, 4(6): 1523-1539. doi: 10.3934/math.2019.6.1523


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