Multiple rogue wave solutions and the linear superposition principle for a (3 + 1)‐dimensional Kadomtsev–Petviashvili–Boussinesq‐like equation arising in energy distributions

Abstract

The multiple exp‐function method and multiple rogue wave solutions method are employed for searching the multiple soliton solutions to the (3 + 1)‐dimensional Kadomtsev–Petviashvili–Boussinesq‐like (KP‐Boussinesq‐like) equation. The obtained solutions contain the first‐order, second‐order, third‐order, and fourth‐order wave solutions. At the critical point, the second‐order derivative and Hessian matrix for only one point are investigated, and the lump solution has one maximum value. Moreover, we employ the linear superposition principle to determine N‐soliton wave solutions of the KP‐Boussinesq‐like equation. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values.