Chin. Phys. B, 2021, Vol. 30(8): 080203    DOI: 10.1088/1674-1056/ac052a
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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

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
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.
Keywords:  forced variable-coefficient extended KdV equation      consistent Riccati expansion      analytic solution      interaction wave solution
Received:  12 January 2021      Revised:  06 April 2021      Accepted manuscript online:  26 May 2021
 PACS: 02.30.Jr (Partial differential equations) 02.20.Hj (Classical groups) 02.20.Sv (Lie algebras of Lie groups) 92.60.hh (Acoustic gravity waves, tides, and compressional waves)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11775047, 11775146, and 11865013).
Corresponding Authors:  Ping Liu     E-mail:  liuping49@126.com