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