一类耦合浅水波方程的解析求解和应用分析
The Analytical Solution and Application of a Coupled Shallow Water Wave Equation
DOI: 10.12677/AAM.2022.115268, PDF,    国家自然科学基金支持
作者: 朴圣斌*：江苏科技大学理学院，江苏 镇江；马 丁：江苏科技大学理学院，江苏 镇江；中南大学物理与电子学院，湖南 长沙；罗文琛：中南大学物理与电子学院，湖南 长沙；周 昱#：江苏科技大学理学院，江苏 镇江；江苏科技大学深蓝学院，江苏 镇江
关键词: 浅水波；解析方法；流体动力学；非线性演化方程；Shallow Water Wave； Analytical Method； Hydrodynamics； Nonlinear Evolution Equation
摘要: 本文通过解析方法求解了一类耦合的非线性浅水波方程并对所得解进行了讨论。研究了不同参数情况下方程解的行为，结论表明频散系数可明显影响浅水波方程的动力学。基于本文给出的方程，讨论了其在特殊参数下的一些拓展应用。本文的结论对浅水波方程有关性质的研究具有一定参考意义。
Abstract: In this paper, solutions of a set of coupled nonlinear shallow water wave equations are solved based on the analytical method, and the results are discussed. The behavior of the equation solution un-der different parameters is studied. We concluded that the dispersion coefficient can significantly affect the dynamics of the shallow water wave. Based on the equations given in this paper, some ex-tended applications under special parameters are discussed. The result presented in this paper may give insights to the relevant studies of the shallow water wave equation.
文章引用：朴圣斌, 马丁, 罗文琛, 周昱. 一类耦合浅水波方程的解析求解和应用分析[J]. 应用数学进展, 2022, 11(5): 2530-2537. https://doi.org/10.12677/AAM.2022.115268

参考文献

[1] Debnath, L. (2012) Nonlinear Partial Differential Equations for Scientists and Engineers. 3rd Edition, Birkhäuser, Boston. [Google Scholar] [CrossRef] 
[2] Arendt, W., Brezis, H. and Pierre, M. (2004) Nonlinear Evolution Equations and Related Topics. Birkhäuser, Basel. [Google Scholar] [CrossRef] 
[3] Pelinovsky, E. and Kharif, C. (Eds.) (2016) Extreme Ocean Waves. Springer, Cham, 12-15. [Google Scholar] [CrossRef] 
[4] Lin, C. and Clark, J. (1959) On the Theory of Shallow Water Waves. Tsing Hua Journal of Chinese Studies, 1, 54-62.
[5] Whitham, G. (1967) Variational Methods and Applica-tions to Water Waves. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 299, 6-25. [Google Scholar] [CrossRef] 
[6] Broer, L. (1975) Approximate Equations for Long Water Waves. Applied Scientific Research, 31, 377-395. [Google Scholar] [CrossRef] 
[7] Kaup, D. (1975) A Higher-Order Water-Wave Equation and the Method for Solving It. Progress of Theoretical Physics, 54, 396-408. [Google Scholar] [CrossRef] 
[8] Zhang, Z.Y., Yong, X.L. and Chen, Y.F. (2008) Symmetry Analysis for Whitham-Broer-Kaup Equations. Journal of Nonlinear Mathematical Physics, 15, 383-397. [Google Scholar] [CrossRef] 
[9] Xu, T.T. (2015) Darboux Transformation and New Multi-Soliton Solutions of the Whitham-Broer-Kaup System. Applied Mathematics, 6, 20-27. [Google Scholar] [CrossRef] 
[10] Fan, E.G. and Zhang, H.Q. (1998) Backlund Transformation and Ex-act Solutions for Whitham-Broer-Kaup Equations in Shallow Water. Applied Mathematics and Mechanics, 19, 713-716. [Google Scholar] [CrossRef] 
[11] Zheng, Z. and Shan, W.R. (2009) Application of Exp-Function Method to the Whitham-Broer-Kaup Shallow Water Model Using Symbolic Computation. Applied Mathematics and Computation, 215, 2390-2396. [Google Scholar] [CrossRef] 
[12] Lou, S.Y. (2015) Consistent Riccati Expansion for Integrable Sys-tems. Studies in Applied Mathematics, 134, 372-402. [Google Scholar] [CrossRef] 

为你推荐