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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering, Benha University, Benha, Egypt

    Mohamed R. Ali

  2. Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, Egypt

    R. Sadat

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Wen-Xiu Ma

  4. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Wen-Xiu Ma

  5. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wen-Xiu Ma

  6. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Wen-Xiu Ma

  7. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Camus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

Authors
  1. Mohamed R. Ali
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  2. R. Sadat
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  3. Wen-Xiu Ma
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Correspondence to Wen-Xiu Ma.

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Ali, M.R., Sadat, R. & Ma, WX. Investigation of new solutions for an extended (2 + 1)-dimensional Calogero-Bogoyavlenskii-Schif equation. Front. Math. China 16, 925–936 (2021). https://doi.org/10.1007/s11464-021-0952-3

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  • DOI: https://doi.org/10.1007/s11464-021-0952-3

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