AIMS Mathematics, 2020, 5(4): 4027-4044. doi: 10.3934/math.2020259

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New dark-bright soliton in the shallow water wave model

1 Final International University, Kyrenia Mersin 10, Turkey
2 Harran University, Faculty of Education, Sanliurfa, Turkey
3 School of Information Science and Technology, Yunnan Normal University, Yunnan, China

In this paper, we employ the sine-Gordon expansion method to shallow water wave models which are Kadomtsev-Petviashvili-Benjamin-Bona-Mahony and the Benney-Luke equations. We construct many new complex combined dark-bright soliton, anti-kink soliton solutions for the governing models. The 2D, 3D and contour plots are given under the suitable coefficients. The obtained results show that the approach proposed for these completely integrable equations can be used effectively.
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