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

Ruijuan Li (), Onur Alp İlhan, Jalil Manafian (), Khaled H. Mahmoud, Mostafa Abotaleb and Ammar Kadi
Additional contact information
Ruijuan Li: School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China
Onur Alp İlhan: Department of Mathematics, Faculty of Education, Erciyes University, Melikgazi, Kayseri 38039, Turkey
Jalil Manafian: Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov Str., Lankaran AZ4200, Azerbaijan
Khaled H. Mahmoud: Department of Physics, College of Khurma University College, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Mostafa Abotaleb: Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia
Ammar Kadi: Department of Food and Biotechnology, South Ural State University, 454080 Chelyabinsk, Russia

Mathematics, 2022, vol. 10, issue 17, 1-17

Abstract: 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.

Keywords: hirota bilinear technique; interaction between a lump and one-, two soliton solutions; generalized shallow water wave equation with variable coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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