New non-traveling wave solutions for (3+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation

Yuanqing Xu; Xiaoxiao Zheng; Jie Xin; Yuanqing Xu; Xiaoxiao Zheng; Jie Xin

doi:10.3934/math.2021182

AIMS Mathematics

2021, Volume 6, Issue 3: 2996-3008. doi: 10.3934/math.2021182

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Research article

New non-traveling wave solutions for (3+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation

1.
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, P. R. China
2.
School of Mathematics and Statistics, Ludong University, Yantai, Shandong 264025, P. R. China
3.
College of Information Science and Engineering, Shandong Agricultural University, Taian, Shandong 271018, P. R. China

Received: 04 November 2020 Accepted: 28 December 2020 Published: 11 January 2021
MSC : 35C99, 35G20, 37K10, 68W30

In this paper, we investigate non-traveling wave solutions of the (3+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa (VC-DJKM) equation, which describes the real physical phenomena owing to the inhomogeneities of media. By combining the extended homoclinic test approach with variable separation method, we obtain abundant new exact non-traveling wave solutions of the (3+1)-dimensional VC-DJKM equation. These results with a parabolic tail or linear tail reveal the complex structure of the solutions for (3+1)-dimensional VC-DJKM equation. Moreover, the tail in these solutions maybe give a prediction of physical phenomenon. When arbitrary functions contained in these non-traveling wave solutions are taken as some special functions, we can get the kink-type solitons, singular solitary wave solutions, and periodic solitary wave solutions, and so on. As the special cases of our work, the corresponding results of (3+1)-dimensional DJKM equation, (2+1)-dimensional DJKM equation, (2+1)-dimensional VC-DJKM equation are also given.
- extended homoclinic test approach,
- variable separation method,
- VC-DJKM equation,
- exact solutions
Citation: Yuanqing Xu, Xiaoxiao Zheng, Jie Xin. New non-traveling wave solutions for (3+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation[J]. AIMS Mathematics, 2021, 6(3): 2996-3008. doi: 10.3934/math.2021182

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Abstract

In this paper, we investigate non-traveling wave solutions of the (3+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa (VC-DJKM) equation, which describes the real physical phenomena owing to the inhomogeneities of media. By combining the extended homoclinic test approach with variable separation method, we obtain abundant new exact non-traveling wave solutions of the (3+1)-dimensional VC-DJKM equation. These results with a parabolic tail or linear tail reveal the complex structure of the solutions for (3+1)-dimensional VC-DJKM equation. Moreover, the tail in these solutions maybe give a prediction of physical phenomenon. When arbitrary functions contained in these non-traveling wave solutions are taken as some special functions, we can get the kink-type solitons, singular solitary wave solutions, and periodic solitary wave solutions, and so on. As the special cases of our work, the corresponding results of (3+1)-dimensional DJKM equation, (2+1)-dimensional DJKM equation, (2+1)-dimensional VC-DJKM equation are also given.

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