Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics

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Manafian J., İlhan O. A. , Avazpour L., Alizadeh A.

Advances in Difference Equations, cilt.2, no.11, ss.1-19, 2021 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 2
  • Basım Tarihi: 2021
  • Dergi Adı: Advances in Difference Equations
  • Sayfa Sayıları: ss.1-19



The Hirota bilinear method is employed for searching the localized waves, lump solitons, and solutions between lumps and rogue waves for the fractional generalized Calogero-Bogoyavlenskii-Schiff_-Bogoyavlensky- Konopelchenko (CBS-BK) equation.

We probe three cases including lump (combination of two positive functions as polynomial), lump-kink (combination of two positive functions as polynomial and exponential function) called the interaction between a lump and one line soliton, and lump-soliton (combination of two positive functions as polynomial and hyperbolic cos function) called the interaction between a lump and two-line solitons. At the critical point, the second-order derivative and the Hessian matrix for only one point will be investigated and the lump solution has one maximum value. The moving path of the lump solution and also, the moving

velocity and the maximum amplitude will be obtained. The graphs for various fractional order _ are plotted to contain 3D plot, contour plot, density plot, and 2D plot. The physical phenomena of this gained lump and its interaction soliton solutions are analyzed and indicated in _gures by selecting the suitable values. That will be extensively used to report many attractive physical phenomena in the _elds of fluid dynamics, classical mechanics, physics, and so on.