Investigation of new solutions for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif equation

doi:10.1007/s11464-021-0952-3

Front. Math. China

2021, Vol. 16

Issue (4) : 925-936 https://doi.org/10.1007/s11464-021-0952-3

RESEARCH ARTICLE

Investigation of new solutions for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif equation

Mohamed R. ALI¹, R. SADAT², Wen-Xiu MA^3,^4,^5,^6,⁷(

)

¹. Department of Mathematics, Faculty of Engineering, Benha University, Egypt
². Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, Egypt
³. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
⁴. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
⁵. Department of Mathematics and Statistics, University of South Florida, Tampa, FL33620-5700, USA
⁶. School of Mathematics, South China University of Technology, Guangzhou 510640, China
⁷. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Camus, Private Bag X2046, Mmabatho 2735, South Africa

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Abstract

We investigate and concentrate on new infinitesimal generators of Lie symmetries for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif (eCBS) equation using the commutator table which results in a system of nonlinear ordinary differential equations (ODEs) which can be manually solved. Through two stages of Lie symmetry reductions, the eCBS equation is reduced to non-solvable nonlinear ODEs using different combinations of optimal Lie vectors. Using the integration method and the Riccati and Bernoulli equation methods, we investigate new analytical solutions to those ODEs. Back substituting to the original variables generates new solutions to the eCBS equation. These results are simulated through three- and two-dimensional plots.

Keywords Extended Calogero-Bogoyavlenskii-Schif (eCBS) equation Riccati-Bernoulli equation symmetry analysis integrating factor nonlinear integrable equations

Corresponding Author(s): Wen-Xiu MA

Issue Date: 11 October 2021

Cite this article:

Mohamed R. ALI,R. SADAT,Wen-Xiu MA. Investigation of new solutions for an extended (2+ 1)-dimensional Calogero-Bogoyavlenskii-Schif equation[J]. Front. Math. China, 2021, 16(4): 925-936.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0952-3
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I4/925

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