Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves

doi:10.1088/1674-1056/ac052a

中国物理B ›› 2021, Vol. 30 ›› Issue (8): 80203-080203.doi: 10.1088/1674-1056/ac052a

Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves

Ping Liu(刘萍)^1,†, Bing Huang(黄兵)², Bo Ren(任博)³, and Jian-Rong Yang(杨建荣)⁴

1 School of Electronic and Information Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China;
2 School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China;
3 Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
4 School of Physics and Electronic Information, Shangrao Normal University, Shangrao 334001, China

收稿日期:2021-01-12 修回日期:2021-04-06 接受日期:2021-05-26 出版日期:2021-07-16 发布日期:2021-08-02
通讯作者: Ping Liu E-mail:liuping49@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775047, 11775146, and 11865013).

Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves

Ping Liu(刘萍)^1,†, Bing Huang(黄兵)², Bo Ren(任博)³, and Jian-Rong Yang(杨建荣)⁴

1 School of Electronic and Information Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China;
2 School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China;
3 Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
4 School of Physics and Electronic Information, Shangrao Normal University, Shangrao 334001, China

Received:2021-01-12 Revised:2021-04-06 Accepted:2021-05-26 Online:2021-07-16 Published:2021-08-02
Contact: Ping Liu E-mail:liuping49@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775047, 11775146, and 11865013).

摘要/Abstract

摘要： We study a forced variable-coefficient extended Korteweg-de Vries (KdV) equation in fluid dynamics with respect to internal solitary wave. Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevé expansion. When the variable coefficients are time-periodic, the wave function evolves periodically over time. Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations. One-parameter group transformations and one-parameter subgroup invariant solutions are presented. Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method. The consistent Riccati expansion (CRE) solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE. Interaction phenomenon between cnoidal waves and solitary waves can be observed. Besides, the interaction waveform changes with the parameters. When the variable parameters are functions of time, the interaction waveform will be not regular and smooth.

关键词: forced variable-coefficient extended KdV equation, consistent Riccati expansion, analytic solution, interaction wave solution

Abstract: We study a forced variable-coefficient extended Korteweg-de Vries (KdV) equation in fluid dynamics with respect to internal solitary wave. Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevé expansion. When the variable coefficients are time-periodic, the wave function evolves periodically over time. Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations. One-parameter group transformations and one-parameter subgroup invariant solutions are presented. Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method. The consistent Riccati expansion (CRE) solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE. Interaction phenomenon between cnoidal waves and solitary waves can be observed. Besides, the interaction waveform changes with the parameters. When the variable parameters are functions of time, the interaction waveform will be not regular and smooth.

Key words: forced variable-coefficient extended KdV equation, consistent Riccati expansion, analytic solution, interaction wave solution

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Hj (Classical groups) 02.20.Sv (Lie algebras of Lie groups) 92.60.hh (Acoustic gravity waves, tides, and compressional waves)

Ping Liu(刘萍), Bing Huang(黄兵), Bo Ren(任博), and Jian-Rong Yang(杨建荣). Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves[J]. 中国物理B, 2021, 30(8): 80203-080203.

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Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves

Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves

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