Interaction characteristics of the Riemann wave propagation in the (2+1)-dimensional generalized breaking soliton system

• Published in: International journal of computer mathematics Vol. 100; no. 6; pp. 1340 - 1355
• Main Authors: Muhamad, Kalsum Abdulrahman, Tanriverdi, Tanfer, Mahmud, Adnan Ahmad, Baskonus, Haci Mehmet
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.06.2023; Taylor & Francis Ltd
• Subjects: 34-04; 65-04; 65-06; Dynamic characteristics; Exponential functions; Generalized breaking soliton system; Graphs; Hyperbolic functions; modified exponential function method; Nonlinear systems; Propagation; Riemann wave propagation; Riemann waves; Software; Solitary waves; soliton solutions; Traveling waves; travelling wave transformation; Wave propagation
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2023.2186775

In this study, the nonlinear (2+1)-dimensional generalized breaking soliton system has been studied by introducing an appropriate travelling wave transformation. The model under consideration is integrable with constant coefficients and demonstrates Riemann wave propagation characteristics, it principally transformed into a third-order nonlinear ODE. The reliable and robust method, namely the modified exponential function method, is applied to the nonlinear system for the first time. The main goal is to investigate and obtain some explicitly exact travelling waves, periodic waves, and soliton solutions. The obtained solutions are in the form of exponential functions, trigonometric hyperbolic functions, and combined structures of the trigonometric hyperbolic with logarithmic functions. Furthermore, the obtained solutions are new and significant in revealing the pertinent features of the physical phenomenon. The results have been expressed in several graphs, including two- and three-dimensional plots, for the best visual assessment of the physical significance and dynamic characteristics. The most potent and efficacious tools are the computer software packages we utilize to derive solutions and graphs.