Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(8): 080203    DOI: 10.1088/1674-1056/ac052a
GENERAL Prev   Next  

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

Cite this article: 

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 2021 Chin. Phys. B 30 080203

[1] Grimshaw R, Pelinovsky E, Stepanyants Y and Talipova T 2006 Mar. Fresh-water Res. 57 265
[2] Liao G H, Yang C H, Xu X H and Shi X G 2012 Acta Oceanol. Sin. 31 26
[3] Chowa K W, Grimshawb R J and Ding E 2005 Wave Motion 43 158
[4] Korteweg D J and de Vries G 1895 Philos. Mag. 39 422
[5] Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[6] Wang M, Tian B, Sun Y and Zhang Z 2020 Comput. Math. Appl. 79 576
[7] Chen Y Q, Tian B, Qu Q X, Li He, Zhao X H, Tian H and Wang M 2020 Int. J. Mod. Phys. B 34 2050226
[8] Zhao X, Tian B, Qu Q X, Yuan Y Q, Du X X and Chu M X 2020 Mod. Phys. Lett. B 34 2050282
[9] Liu Y, Gao Y T, Sun Z Y and Yu X 2011 Nonlinear Dyn. 66 575
[10] Zhang S, Chen M T and Qian W Y 2015 Therm. Sci. 19 1223
[11] Grimshaw R, Pelinovsky E, Talipova T and Kurkin A 2004 J. Phys. Oceanogr. 34 2774
[12] Grimshaw R H, Pelinovsky E and Talipova T 1999 Physica D 132 40
[13] Tay K G, Ong C T and Mohamad M N 2007 Int. J. Eng. Sci. 45 339
[14] Gao X Y, Guo Y J and Shan W R 2020 Eur. Phys. J. Plus 135 689
[15] Gao X Y, Guo Y J and Shan W R 2020 Appl. Math. Lett. 104 106170
[16] Gao X Y, Guo Y J and Shan W R 2020 Chaos, Solitons and Fractals 138 109950
[17] Du X X, Tian B, Qu Q X, Yuan Y Q and Zhao X H 2020 Chaos, Solitons and Fractals 134 109709
[18] Olver P 1986 Applications of Lie Group to Differential Equations (New York: Spring-Verlag)
[19] Liu P, Wang J H, and Zhang H B 2020 Wave Random Complex 30 216
[20] Liu P, Cheng J, Ren B and Yang J R 2020 Chin. Phys. B 29 020201
[21] Liu P, Xu H R and Yang J R 2020 Acta Phys. Sin. 69 010203 (in Chinesen)
[22] Lou S Y 2015 Stud. Appl. Math. 134 372
[23] Chen S S, Tian B, Chai J, Wu X Y and Du Z 2020 Wave Random Complex 30 389
[24] Zhang C R, Tian B, Qu Q X, Liu L and Tian H Y 2020 Z. Angew. Math. Phys. 71 18
[25] Guo B X, Gao Z J and Lin J 2016 Commun. Theor. Phys. 66 589
[26] Liu Y K and Li B 2016 Chin. J. Phys. 54 718
[27] Wang X B, Jia M and Lou S Y 2021 Chin. Phys. B 30 010501
[28] Liu P and Fu P K 2011 Chin. Phys. B 20 090203
[29] Hu H C and Liu F Y 2020 Chin. Phys. B 29 040201
[1] Lump and interaction solutions to the (3+1)-dimensional Burgers equation
Jian Liu(刘健), Jian-Wen Wu(吴剑文). Chin. Phys. B, 2020, 29(3): 030201.
[2] Bäcklund transformations, consistent Riccati expansion solvability, and soliton-cnoidal interaction wave solutions of Kadomtsev-Petviashvili equation
Ping Liu(刘萍), Jie Cheng(程杰), Bo Ren(任博), Jian-Rong Yang(杨建荣). Chin. Phys. B, 2020, 29(2): 020201.
[3] Soliton-cnoidal interactional wave solutions for the reduced Maxwell-Bloch equations
Li-Li Huang(黄丽丽), Zhi-Jun Qiao(乔志军), Yong Chen(陈勇). Chin. Phys. B, 2018, 27(2): 020201.
[4] Nonlocal symmetry and exact solutions of the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation
Li-Li Huang(黄丽丽), Yong Chen(陈勇). Chin. Phys. B, 2016, 25(6): 060201.
[5] Nonlinear tunneling through a strong rectangular barrier
Zhang Xiu-Rong (张秀荣), Li Wei-Dong (李卫东). Chin. Phys. B, 2015, 24(7): 070311.
[6] The consistent Riccati expansion and new interaction solution for a Boussinesq-type coupled system
Ruan Shao-Qing (阮少卿), Yu Wei-Feng (余炜沣), Yu Jun (俞军), Yu Guo-Xiang (余国祥). Chin. Phys. B, 2015, 24(6): 060201.
[7] Heat transfer analysis in the flow of Walters’B fluid with a convective boundary condition
T. Hayat, Sadia Asad, M. Mustafa, Hamed H. Alsulami. Chin. Phys. B, 2014, 23(8): 084701.
[8] Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer
Krishnendu Bhattacharyya, Tasawar Hayat, Ahmed Alsaedi. Chin. Phys. B, 2013, 22(2): 024702.
[9] Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation
Zhao Guo-Zhong (赵国忠), Yu Xi-Jun (蔚喜军), Xu Yun (徐云), Zhu Jiang (朱江), Wu Di (吴迪). Chin. Phys. B, 2010, 19(8): 080204.
[10] Variational iteration method for solving compressible Euler equations
Zhao Guo-Zhong (赵国忠), Yu Xi-Jun (蔚喜军), Xu Yun (徐云), Zhu Jiang (朱江). Chin. Phys. B, 2010, 19(7): 070203.
[11] New approximate solution for time-fractional coupled KdV equations by generalised differential transform method
Liu Jin-Cun(刘金存) and Hou Guo-Lin(侯国林). Chin. Phys. B, 2010, 19(11): 110203.
[12] Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field
Ni Gu-Yan(倪谷炎), Yan Li(颜力), and Yuan Nai-Chang(袁乃昌). Chin. Phys. B, 2008, 17(10): 3629-3634.
No Suggested Reading articles found!