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The geophysical KdV equation: its solitons, complexiton, and conservation laws

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Abstract

The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. More precisely, specific transformations are first adopted to derive one-dimensional and operator forms of the governing model. Solitons and complexiton of the geophysical KdV equation are then retrieved with the help of several well-established approaches such as the Kudryashov and Hirota methods. In the end, the new conservation theorem given by Ibragimov is formally employed to extract conservation laws of the governing model. It is shown that by increasing the Coriolis parameter, based on the selected parameter regimes, less time is needed for tending the free surface elevation to zero.

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Authors and Affiliations

  1. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

    K. Hosseini

  2. Department of Mathematics, Near East University TRNC, Mersin 10, Turkey

    K. Hosseini

  3. Department of Mathematics - Computer, Art-Science Faculty, Eskisehir Osmangazi University, Eskisehir, Turkey

    A. Akbulut

  4. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey

    D. Baleanu

  5. Institute of Space Sciences, Magurele-Bucharest, Romania

    D. Baleanu

  6. Department of Medical Research, China Medical University, Taichung, 40447, Taiwan

    D. Baleanu

  7. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    S. Salahshour

  8. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, 44891-63157, Iran

    M. Mirzazadeh

  9. Department of Mathematics, Lafayette College, Easton, PA, USA

    L. Akinyemi

Authors
  1. K. Hosseini
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  2. A. Akbulut
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  3. D. Baleanu
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  4. S. Salahshour
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  5. M. Mirzazadeh
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  6. L. Akinyemi
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Correspondence to K. Hosseini or D. Baleanu.

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Hosseini, K., Akbulut, A., Baleanu, D. et al. The geophysical KdV equation: its solitons, complexiton, and conservation laws. Int J Geomath 13, 12 (2022). https://doi.org/10.1007/s13137-022-00203-8

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  • DOI: https://doi.org/10.1007/s13137-022-00203-8

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