Exact solutions of a class of nonlinear dispersive long wave systems via Feng's first integral method

Qiuci Lu; Songchuan Zhang; Hang Zheng; Qiuci Lu; Songchuan Zhang; Hang Zheng

doi:10.3934/math.2021464

AIMS Mathematics

2021, Volume 6, Issue 8: 7984-8000. doi: 10.3934/math.2021464

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Research article

Exact solutions of a class of nonlinear dispersive long wave systems via Feng's first integral method

1.
School of Humanities and Teacher Education of Wuyi University, Wuyishan, Fujian 354300, China
2.
School of Mathematics and Computer, Wuyi University, Wu Yishan, Fujian 354300, China

Received: 23 March 2021 Accepted: 11 May 2021 Published: 21 May 2021
MSC : 35A09, 35A24, 35C07, 35C08, 35F50, 35G50

In this paper, eight groups of exact solutions for the (1+1)-dimensional and (2+1)-dimensional nonlinear dispersive long wave systems are found respectively via Feng's first integral method. It is shown that there are some similarities in the expressions of the solutions of (1+1)-dimensional and (2+1)-dimensional DLWEs, while there exist some differences in their dimensions and their physical significance. Finally, some graphs are presented to show these features, which also show the effectiveness of the proposed method.
- exact solutions,
- Feng's first integral method,
- nonlinear dispersive long wave equations,
- division theorem
Citation: Qiuci Lu, Songchuan Zhang, Hang Zheng. Exact solutions of a class of nonlinear dispersive long wave systems via Feng's first integral method[J]. AIMS Mathematics, 2021, 6(8): 7984-8000. doi: 10.3934/math.2021464

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Abstract

In this paper, eight groups of exact solutions for the (1+1)-dimensional and (2+1)-dimensional nonlinear dispersive long wave systems are found respectively via Feng's first integral method. It is shown that there are some similarities in the expressions of the solutions of (1+1)-dimensional and (2+1)-dimensional DLWEs, while there exist some differences in their dimensions and their physical significance. Finally, some graphs are presented to show these features, which also show the effectiveness of the proposed method.

References

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