Journal
MATHEMATICS
Volume 10, Issue 17, Pages -Publisher
MDPI
DOI: 10.3390/math10173074
Keywords
hirota bilinear technique; interaction between a lump and one-; two soliton solutions; generalized shallow water wave equation with variable coefficients
Categories
Funding
- Taif University, Taif, Saudi Arabia [TURSP-2020/162]
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In this paper, the exact solutions of the (3+1)-dimensional variable-coefficient generalized shallow water wave equation are studied using the Hirota bilinear method. Multiple rational solutions are obtained by selecting different interactions. The method shows progress in solving extended homoclinic breather wave solutions and presents the results in different graphical forms.
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- or two-soliton solutions are obtained. The bilinear form is considered in terms of Hirota derivatives. Accordingly, the logarithm algorithm to obtain the exact solutions of a (3+1)-dimensional variable-coefficient (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 mathematical 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 effect of the free parameters on the behavior of acquired figures to a few obtained solutions for two nonlinear rational exact cases was also discussed.
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