New dark-bright soliton in the shallow water wave model

Gulnur Yel; Haci Mehmet Baskonus; Wei Gao; Gulnur Yel; Haci Mehmet Baskonus; Wei Gao

doi:10.3934/math.2020259

AIMS Mathematics

2020, Volume 5, Issue 4: 4027-4044. doi: 10.3934/math.2020259

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Research article

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

Received: 17 October 2019 Accepted: 20 April 2020 Published: 27 April 2020
MSC : 35C08, 35Q51

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.
- the sine-Gordon expansion method,
- Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation,
- Benney-Luke equation,
- solitary wave solutions
Citation: Gulnur Yel, Haci Mehmet Baskonus, Wei Gao. New dark-bright soliton in the shallow water wave model[J]. AIMS Mathematics, 2020, 5(4): 4027-4044. doi: 10.3934/math.2020259

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Abstract

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.

References

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