Integrability and multiple-rogue and multi-soliton wave solutions of the (3+1)-dimensional Hirota–Satsuma–Ito equation

This paper constructs a new [Formula: see text]-dimensional Hirota–Satsuma–Ito equation and employs the Hirota N-soliton condition to determine the conditions for the existence of N-soliton solutions. Under these conditions, the Hirota bilinear method is utilized to derive N-soliton solutions of the equation. Additionally, breather solutions of the equation are obtained through constraints on complex conjugate parameters, while lump solutions are derived using the long-wave limit method. Building upon these results, interaction solutions are also explored. Furthermore, through the multiple-rogue wave method, multi-rogue wave solutions of the [Formula: see text]-dimensional Hirota–Satsuma–Ito equation are investigated. A comparison between lump solutions obtained via the Hirota bilinear method and the multi-rogue wave solutions from multiple-rogue wave method reveals significant discrepancies.