A study on soliton, lump solutions to a generalized (3+1)-dimensional Hirota--Satsuma--Ito equation

Abstract

In this article, through the Hirota bilinear method and long wave limit method, based on the N-solitons, we construct the multiple lump solutions of the generalized (3+1)-dimensional Hirota–Satsuma–Ito equation. Furthermore, to enhance our understanding of the solutions obtained, we further elucidate the physical implications of these solutions with three-dimensional and two-dimensional graphs. The solutions obtained might have practical applications in elucidating the dynamic behaviors of higher-dimensional systems, particularly in the study area of waves in shallow water and the study of nonlinear optics.

Keywords

• hirota bilinear
• long wave limit
• generalized (3+1)-dimensional hirota–satsuma–ito equation
• multiple lump solutions