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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Page 1533 (Mi zvmmf11131)  

Analytical study on the generalized fifth-order Kaup–Kupershmidt equation from the shallow water wave

Pan Wanga, Jian-Rong Yanga, Li Chena, Sheng-Xin Lib, Feng-Hua Qic

a Sports Business School, Beijing Sport University, Information Road Haidian District 100084 Beijing, No. 48, China
b School of Management, Beijing Sport University, Information Road Haidian District 100084 Beijing, No. 48, China
c School of Information, Beijing Wuzi University 101149 Beijing, China

Abstract: In this paper, the generalized fifth-order Kaup–Kupershmidt (KK) equation from the shallow water wave, have been investigated. With the help of bilinear method and auxiliary function, the multi-soliton solutions of the generalized fifth-order KK equation have been obtained, and those solutions have not been given before. From the analytical view, the interactions of the solitons have been presented. Through the discussion, we have found that the velocity of the soliton is related to the sign of the physical parameters $b$ and ${{c}_{j}}$. Also, the (bright or dark-like) types of the soliton interaction are related to the physical parameters $a$. Hence, the velocities and bright-dark types of the soliton interactions could be controlled by adjusting the physical parameters.

Key words: Nonlinear fifth-order Kaup–Kupershmidt equation, Soliton solutions, bilinear method, Auxiliary function.

Funding Agency
This work has been supported by the National Natural Science Foundation of China under grant nos. 11426041 and 11605011.


DOI: https://doi.org/10.31857/S0044466920090161


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1480–1487

Bibliographic databases:

Received: 31.05.2019
Revised: 12.01.2020
Accepted:09.04.2020
Language:

Citation: Pan Wang, Jian-Rong Yang, Li Chen, Sheng-Xin Li, Feng-Hua Qi, “Analytical study on the generalized fifth-order Kaup–Kupershmidt equation from the shallow water wave”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1533; Comput. Math. Math. Phys., 60:9 (2020), 1480–1487

Citation in format AMSBIB
\Bibitem{WanYanChe20}
\by Pan~Wang, Jian-Rong~Yang, Li~Chen, Sheng-Xin~Li, Feng-Hua~Qi
\paper Analytical study on the generalized fifth-order Kaup--Kupershmidt equation from the shallow water wave
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 9
\pages 1533
\mathnet{http://mi.mathnet.ru/zvmmf11131}
\crossref{https://doi.org/10.31857/S0044466920090161}
\elib{https://elibrary.ru/item.asp?id=43832511}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 9
\pages 1480--1487
\crossref{https://doi.org/10.1134/S0965542520090158}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094665069}


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