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

Abstract

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.

Keywords:

• Generalized breaking soliton system
• travelling wave transformation
• modified exponential function method
• Riemann wave propagation
• soliton solutions

Mathematics Subject Classifications:

• 34-04
• 65-04
• 65-06

Acknowledgments

The authors investigated the research model, developed applications, and performed calculations. All authors contributed equally to the writing of the paper and equally to the assessment of the results.

Disclosure statement

The authors declare that there is no conflict of interest regarding the publication of this paper.

Data availability statement

There are no related data with this paper, or the data will not be deposited. For ethical and legal reasons, the data produced and/or evaluated during the present investigations are not publicly accessible, but they are available from the relevant author upon justifiable request.