Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation

Tianwei Qiu, Zhen Wang (), Xiangyu Yang, Guangmei Wei and Fangsen Cui
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Tianwei Qiu: School of Mathematics Sciences, Beihang University, Beijing 100191, China
Zhen Wang: School of Mathematics Sciences, Beihang University, Beijing 100191, China
Xiangyu Yang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Guangmei Wei: School of Mathematics Sciences, Beihang University, Beijing 100191, China
Fangsen Cui: Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore

Mathematics, 2024, vol. 12, issue 19, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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