On the Oceanic/Laky Shallow-Water Dynamics through a Boussinesq-Burgers System

被引：10
作者：
Gao, Xin-Yi [1 ,2 ,3 ]
Guo, Yong-Jiang [1 ,2 ]
Shan, Wen-Rui [1 ,2 ]
机构：
[1] Beijing Univ Posts & Telecommun, State Key Lab Informat Photon & Opt Commun, Beijing 100876, Peoples R China
[2] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China
[3] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
来源：
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Ocean beaches; Lakes; Shallow-water waves; Boussinesq-Burgers system; Computerized symbolic computation; Hetero-Backlund transformation; Similarity reduction; 35-xx; 03Cxx; 70-XX; 76-XX; MULTISOLITON SOLUTIONS; REDUCTIONS;
D O I：
10.1007/s12346-023-00905-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Motivation/Development: In order to investigate the shallow-water waves, researchers have introduced many nice models, e.g., a Boussinesq-Burgers system for cetain shallow-water waves near an ocean beach/inside a lake, which we study here via computerized symbolic computation. Originality/Novelty with Potential Application: Concerning the height deviating from the equilibrium position of water as well as the field of horizontal velocity, we now construct a hetero-Backlund transformation coupling that system to a known partial differential system, as well as two sets of the similarity reductions, starting at that system towards a known ordinary differential equation. Both our hetero-Backlund transformation and similarity reductions lean upon the dispersive power in the shallow water. Results could help the further study on the oceanic/laky shallow-water dynamics.
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收藏
页数：11
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共 60 条
[1]   New Reductions of the Unsteady Axisymmetric Boundary Layer Equation to ODEs and Simpler PDEs [J].
Aksenov, Alexander, V ;
Kozyrev, Anatoly A. .
MATHEMATICS, 2022, 10 (10)
[2]   Integrable system modelling shallow water waves: Kaup-Boussinesq shallow water system [J].
Bhrawy, A. H. ;
Tharwat, M. M. ;
Abdelkawy, M. A. .
INDIAN JOURNAL OF PHYSICS, 2013, 87 (07) :665-671
[3]   Wronskian solutions and Pfaffianization for a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation in a fluid or plasma [J].
Cheng, Chong-Dong ;
Tian, Bo ;
Zhou, Tian-Yu ;
Shen, Yuan .
PHYSICS OF FLUIDS, 2023, 35 (03)
[4]   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)
[5]   NEW SIMILARITY REDUCTIONS OF THE BOUSSINESQ EQUATION [J].
CLARKSON, PA ;
KRUSKAL, MD .
JOURNAL OF MATHEMATICAL PHYSICS, 1989, 30 (10) :2201-2213
[6]   Breather Wave Solutions for the (3+1)-D Generalized Shallow Water Wave Equation with Variable Coefficients [J].
Dawod, Lafta Abed ;
Lakestani, Mehrdad ;
Manafian, Jalil .
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2023, 22 (04)
[7]   Hybrid waves for a (2+1)-dimensional extended shallow water wave equation [J].
Deng, Gao-Fu ;
Gao, Yi-Tian ;
Yu, Xin ;
Ding, Cui-Cui ;
Jia, Ting-Ting ;
Li, Liu-Qing .
PHYSICS OF FLUIDS, 2021, 33 (11)
[8]   Nonlocal symmetries, conservation laws and interaction solutions for the classical Boussinesq-Burgers equation [J].
Dong, Min-Jie ;
Tian, Shou-Fu ;
Yan, Xue-Wei ;
Zhang, Tian-Tian .
NONLINEAR DYNAMICS, 2019, 95 (01) :273-291
[9]   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)
[10]   Lump and hybrid solutions for a (3+1)-dimensional Boussinesq-type equation for the gravity waves over a water surface [J].
Feng, Chun-Hui ;
Tian, Bo ;
Yang, Dan-Yu ;
Gao, Xiao-Tian .
CHINESE JOURNAL OF PHYSICS, 2023, 83 :515-526
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