In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation

被引：66
作者：
Gao, Xin-yi [1 ,2 ,3 ]
机构：
[1] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
[2] North China Univ Technol, Beijing Key Lab Integrat & Anal Large Scale Stream, Beijing 100144, Peoples R China
[3] Beijing Municipal Educ Commiss, Beijing Lab New Energy Storage Technol, Beijing 102206, Peoples R China
来源：
CHINA OCEAN ENGINEERING | 2025年 / 39卷 / 01期
关键词：
ocean; river; extended time-dependent (3+1)-dimensional shallow water wave equation; bilinear auto-B & auml; cklund transformation; similarity reduction; symbolic computation;
D O I：
10.1007/s13344-025-0012-y
中图分类号：
TU [建筑科学];
学科分类号：
0813 ;
摘要：
With respect to oceanic fluid dynamics, certain models have appeared, e.g., an extended time-dependent (3+1)-dimensional shallow water wave equation in an ocean or a river, which we investigate in this paper. Using symbolic computation, we find out, on one hand, a set of bilinear auto-B & auml;cklund transformations, which could connect certain solutions of that equation with other solutions of that equation itself, and on the other hand, a set of similarity reductions, which could go from that equation to a known ordinary differential equation. The results in this paper depend on all the oceanic variable coefficients in that equation.
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收藏
页码：160 / 165
页数：6
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[1]   Elastic collision between one lump wave and multiple stripe waves of nonlinear evolution equations [J].
Chen, Si-Jia ;
Yin, Yu-Hang ;
Lu, Xing .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 130
[2]   Wronskian solutions and linear superposition of rational solutions to B-type Kadomtsev-Petviashvili equation [J].
Chen, Yu ;
Lu, Xing .
PHYSICS OF FLUIDS, 2023, 35 (10)
[3]   Application of femtosecond mode-locked SnTe thin films and generation of bound-state solitons [J].
Chen, Yueqian ;
Wu, Zhitao ;
Xiao, Peiyao ;
Xiao, Wende ;
Liu, Wenjun .
OPTICS LETTERS, 2024, 49 (09) :2437-2440
[4]   Nonlinear localized waves and their interactions for a (2+1)-dimensional extended Bogoyavlenskii-Kadomtsev-Petviashvili equation in a fluid [J].
Cheng, Chong-Dong ;
Tian, Bo ;
Zhou, Tian-Yu ;
Shen, Yuan .
WAVE MOTION, 2024, 125
[5]   Bilinear form, auto-Backlund transformations, Pfaffian, soliton, and breather solutions for a (3+1)-dimensional extended shallow water wave equation [J].
Cheng, Chong-Dong ;
Tian, Bo ;
Shen, Yuan ;
Zhou, Tian-Yu .
PHYSICS OF FLUIDS, 2023, 35 (08)
[6]   Pfaffian, breather, and hybrid solutions for a (2+1)-dimensional generalized nonlinear system in fluid mechanics and plasma physics [J].
Cheng, Chong-Dong ;
Tian, Bo ;
Ma, Yong-Xin ;
Zhou, Tian-Yu ;
Shen, Yuan .
PHYSICS OF FLUIDS, 2022, 34 (11)
[7]   NEW SIMILARITY REDUCTIONS OF THE BOUSSINESQ EQUATION [J].
CLARKSON, PA ;
KRUSKAL, MD .
JOURNAL OF MATHEMATICAL PHYSICS, 1989, 30 (10) :2201-2213
[8]   An extended (3+1)-dimensional Jimbo-Miwa equation: Symmetry reductions, invariant solutions and dynamics of different solitary waves [J].
Dhiman, Shubham Kumar ;
Kumar, Sachin ;
Kharbanda, Harsha .
MODERN PHYSICS LETTERS B, 2021, 35 (34)
[9]   Bilinear Bäcklund Transformation, Fission/Fusion and Periodic Waves of a (3+1)-dimensional Kadomtsev-Petviashvili Equation for the Shallow Water Waves [J].
Feng, Chun-Hui ;
Tian, Bo ;
Gao, Xiao-Tian .
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2024, 63 (03)
[10]   Bilinear Form, Bilinear Backlund Transformations, Breather and Periodic-Wave Solutions for a (2+1)-Dimensional Shallow Water Equation with the Time-Dependent Coefficients [J].
Feng, Chun-Hui ;
Tian, Bo ;
Yang, Dan-Yu ;
Gao, Xiao-Tian .
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2023, 22 (04)
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