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


Hosseini K., AKBULUT A., BALEANU D., SALAHSHOUR S., Mirzazadeh M., Akinyemi L.

GEM - INTERNATIONAL JOURNAL ON GEOMATHEMATICS, vol.13, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13
  • Publication Date: 2022
  • Doi Number: 10.1007/s13137-022-00203-8
  • Journal Name: GEM - INTERNATIONAL JOURNAL ON GEOMATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index, Scopus, Compendex, Geobase, zbMATH
  • Keywords: Geophysical KdV equation, Coriolis parameter, Kudryashov and Hirota methods, Solitons and complexiton, Ibragimov theorem, Conservation laws, PARTIAL-DIFFERENTIAL-EQUATIONS, EVOLUTION-EQUATIONS, WAVE SOLUTIONS, SYMMETRIES

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.