New interaction solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation

Abstract

This study aims to determine novel analytical lump solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation through conducting symbolic computations using the Hirota direct method. This nonlinear model describes the propagation of unidirectional shallow-water waves and interactions of two long waves with different dispersion forms. Some informative descriptions of physical behavior related to the solutions obtained in this article have also been included through several 3D figures and 2D contour plots. The acquired results in this research may be beneficial for better understanding the interaction phenomena of localized nonlinear waves in different research fields of nonlinear science. It is notable that the use of computer algebra in the calculations required by the article is inevitable. Accordingly, in this work, we have used the symbolic package Mathematica. Our results will be meaningful for the investigation of the future development of lump solitons in many physical systems.

Keywords

• Hirota’s bilinear method
• Hirota–Satsuma–Ito equation
• Long waves
• Shallow-water waves
• Computations