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

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 stabili...

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Bibliographic Details
Published inAIMS mathematics Vol. 4; no. 6; pp. 1523 - 1539
Main Authors Ghanbari, Behzad, Inc, Mustafa, Yusuf, Abdullahi, Baleanu, Dumitru
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2019
Subjects
Benney-Luke equation
GERFM
Phi-4 equation
stability analysis
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2019.6.1523