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Solitary Wave Solutions to the Modified Zakharov–Kuznetsov and the (2 + 1)‐Dimensional Calogero–Bogoyavlenskii–Schiff Models in Mathematical Physics

Author

Listed:
  • M. Al-Amin
  • M. Nurul Islam
  • Onur Alp İlhan
  • M. Ali Akbar
  • Danyal Soybaş

Abstract

The modified Zakharov–Kuznetsov (mZK) and the (2 + 1)‐dimensional Calogero–Bogoyavlenskii–Schiff (CBS) models convey a significant role to instruct the internal structure of tangible composite phenomena in the domain of two‐dimensional discrete electrical lattice, plasma physics, wave behaviors of deep oceans, nonlinear optics, etc. In this article, the dynamic, companionable, and further broad‐spectrum exact solitary solitons are extracted to the formerly stated nonlinear models by the aid of the recently enhanced auxiliary equation method through the traveling wave transformation. The implication of the soliton solutions attained with arbitrary constants can be substantial to interpret the involuted phenomena. The established soliton solutions show that the approach is broad‐spectrum, efficient, and algebraic computing friendly and it may be used to classify a variety of wave shapes. We analyze the achieved solitons by sketching figures for distinct values of the associated parameters by the aid of the Wolfram Mathematica program.

Suggested Citation

  • M. Al-Amin & M. Nurul Islam & Onur Alp İlhan & M. Ali Akbar & Danyal Soybaş, 2022. "Solitary Wave Solutions to the Modified Zakharov–Kuznetsov and the (2 + 1)‐Dimensional Calogero–Bogoyavlenskii–Schiff Models in Mathematical Physics," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:5224289
    DOI: 10.1155/2022/5224289
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    References listed on IDEAS

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    1. Hasibun Naher & Farah Aini Abdullah, 2012. "The Improved ( ð º â€² / ð º ) -Expansion Method for the (2+1)-Dimensional Modified Zakharov-Kuznetsov Equation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, August.
    2. Bin Zheng & Qinghua Feng, 2014. "The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, June.
    3. Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    5. Bin Zheng & Qinghua Feng, 2014. "The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Hasibun Naher & Farah Aini Abdullah, 2012. "The Improved (G’/G)‐Expansion Method for the (2+1)‐Dimensional Modified Zakharov‐Kuznetsov Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
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