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Exact solutions for the improved mKdv equation with conformable derivative by using the Jacobi elliptic function expansion method

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Abstract

The goal of this paper is to find exact solutions to the improved modified Korteweg-de Vries (mKdV) equation with a conformable derivative using the Jacobi elliptic function expansion method. The improved mKdV equation is a prominent mathematical model in the realm of nonlinear partial differential equations, with widespread applicability in diverse scientific and engineering domains. This study leverages the well-known effectiveness of the Jacobi elliptic function expansion method in solving nonlinear differential equations, specifically focusing on the intricacies of the improved mKdV problem. The investigation reveals innovative and explicit solutions, providing insight into the dynamics of the related physical processes. This paper provides a comprehensive examination of these solutions, emphasizing their distinct features and depictions using Jacobi elliptic functions. These findings are especially advantageous for specialists in the fields of nonlinear science and mathematical physics, providing significant insights into the behavior and development of nonlinear waves in various physical situations. This work also contributes to our knowledge of the improved mKdV equation and shows that the Jacobi elliptic function expansion method is a useful tool for solving complex nonlinear situations. The study is enhanced with graphical illustrations of various solutions, which further enhance its analytical complexity.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Aamir Farooq & Wen Xiu Ma

  2. Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

    Muhammad Ishfaq Khan

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

    Wen Xiu Ma

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

    Wen Xiu Ma

  5. Material Science Innovation and Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wen Xiu Ma

Authors
  1. Aamir Farooq
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  2. Muhammad Ishfaq Khan
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  3. Wen Xiu Ma
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Contributions

AF: Writing: Original Draft, Writing: Review and Editing, Software, Conceptualisation. MIK: Writing: Review and Editing, Methodology, Formal Analysis. WXM: Revised and Editing.

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Correspondence to Aamir Farooq.

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Farooq, A., Khan, M.I. & Ma, W.X. Exact solutions for the improved mKdv equation with conformable derivative by using the Jacobi elliptic function expansion method. Opt Quant Electron 56, 542 (2024). https://doi.org/10.1007/s11082-023-06258-7

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