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; Fangsen Cui

doi:10.3390/math12193054

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
, Fangsen Cui

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University
Dalian University of Technology
Agency for Science, Technology and Research, Singapore

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Article number	3054
Journal	Mathematics
Volume	12
Issue number	19
DOIs	https://doi.org/10.3390/math12193054
State	Published - Oct 2024

Keywords

(2+1)-dimensional shallow-water wave
Hirota’s bilinear method
lump waves
lump-solitary interaction

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10.3390/math12193054

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

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 = "(2+1)-dimensional shallow-water wave, Hirota{\textquoteright}s bilinear method, lump waves, lump-solitary interaction",

author = "Tianwei Qiu and Zhen Wang and Xiangyu Yang and Guangmei Wei and Fangsen Cui",

note = "Publisher Copyright: {\textcopyright} 2024 by the authors.",

year = "2024",

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doi = "10.3390/math12193054",

language = "英语",

volume = "12",

journal = "Mathematics",

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T1 - Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation

AU - Qiu, Tianwei

AU - Wang, Zhen

AU - Yang, Xiangyu

AU - Wei, Guangmei

AU - Cui, Fangsen

PY - 2024/10

Y1 - 2024/10

N2 - 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.

AB - 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.

KW - (2+1)-dimensional shallow-water wave

KW - Hirota’s bilinear method

KW - lump waves

KW - lump-solitary interaction

UR - https://www.scopus.com/pages/publications/85206575351

U2 - 10.3390/math12193054

DO - 10.3390/math12193054

M3 - 文章

AN - SCOPUS:85206575351

SN - 2227-7390

VL - 12

JO - Mathematics

JF - Mathematics

IS - 19

M1 - 3054

ER -

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

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Keywords

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