A Mathematical Study of the (3+1)-D Variable Coecients Generalized Shallow Water Wave Equation with its Application in the Interaction between the lump and Soliton Solutions

Li R., İlhan O. A. , Manafian J., Mahmoud K., Abotaleb M., Kadi A.

MATHEMATICS, vol.10, no.16, pp.1-17, 2022 (Journal Indexed in SCI Expanded)

  • Publication Type: Article / Article
  • Volume: 10 Issue: 16
  • Publication Date: 2022
  • Title of Journal : MATHEMATICS
  • Page Numbers: pp.1-17



In this paper, the Hirota bilinear method which is an important scheme is used. The equation of the shallow water wave

in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes

of rational solutions by selecting the interaction between a lump and one-, two soliton solutions are obtained. The bilinear

form is considered in terms of Hirota derivatives. Accordingly, the logarithm algorithm to get the exact solutions of (3+1)-

dimensional variable-coecient (VC) generalized shallow water wave equation is utilized. The analytical treatment of extended

homoclinic breather wave solutions is studied and plotted in three forms 3D, 2D, and density plots. Using suitable mathe-

matical assumptions, the established solutions are included in view of a combination of two periodic and two solitons in terms

of two trigonometric and two hyperbolic functions for the governing equation. Maple software for computing the complicated

calculations of nonlinear algebra equations is used. The e ect of the free parameters on the behavior of acquired Figures to a

few obtained solutions for two nonlinear rational exact cases was also discussed.