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

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

MATHEMATICS, cilt.10, sa.17, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 17
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3390/math10173074
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: hirota bilinear technique, interaction between a lump and one-, two soliton solutions, generalized shallow water wave equation with variable coefficients
  • Erciyes Üniversitesi Adresli: Evet

Özet

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.