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Volume 12
Issue 19
10.3390/math12193054
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Solitons, Lumps, Breathers, and Interaction Phenomena for a (21)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation+

by
Tianwei Qiu
1,
Zhen Wang
1,2,*,
Xiangyu Yang
2,
Guangmei Wei
1 and
Fangsen Cui
3
1
School of Mathematics Sciences, Beihang University, Beijing 100191, China
2
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
3
Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(19), 3054; https://doi.org/10.3390/math12193054 (registering DOI)
Submission received: 28 August 2024 / Revised: 26 September 2024 / Accepted: 27 September 2024 / Published: 29 September 2024
(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 2nd Edition)
Versions Notes

Abstract

In this paper, soliton solutions, lump solutions, breather solutions, and lump-solitary wave solutions of a (2+1)-dimensional variable-coefficient extended shallow-water wave (vc-eSWW) equation are obtained based on its bilinear form. By calculating the vector field of the potential function, the interaction between lump waves and solitary waves is studied in detail. Lumps can emerge from the solitary wave and are semi-localized in time. The analytical solutions may enrich our understanding of the nature of shallow-water waves.
Keywords: lump waves; lump-solitary interaction; (2+1)-dimensional shallow-water wave; Hirota’s bilinear method lump waves; lump-solitary interaction; (2+1)-dimensional shallow-water wave; Hirota’s bilinear method

Share and Cite

MDPI and ACS Style

Qiu, T.; Wang, Z.; Yang, X.; Wei, G.; Cui, F. Solitons, Lumps, Breathers, and Interaction Phenomena for a (21)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation+. Mathematics 2024, 12, 3054. https://doi.org/10.3390/math12193054

AMA Style

Qiu T, Wang Z, Yang X, Wei G, Cui F. Solitons, Lumps, Breathers, and Interaction Phenomena for a (21)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation+. Mathematics. 2024; 12(19):3054. https://doi.org/10.3390/math12193054

Chicago/Turabian Style

Qiu, Tianwei, Zhen Wang, Xiangyu Yang, Guangmei Wei, and Fangsen Cui. 2024. "Solitons, Lumps, Breathers, and Interaction Phenomena for a (21)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation+" Mathematics 12, no. 19: 3054. https://doi.org/10.3390/math12193054

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