Multiple rogue wave, dark, bright, and solitary wave solutions to the KP–BBM equation

Under investigation in this paper is the ( 2 + 1 ) -dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation. Based on bilinear method, the multiple rogue wave solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions in the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained, via Maple 18. By utilizing improved tan ( Φ ( ρ ) ∕ 2 ) -expansion technique the series of novel exact solutions in terms of rational, periodic and hyperbolic functions for the fractional cases are derived. Also, the semi-inverse variational principle is offered to get the solitary solutions. We construct the exact lump and rogue wave solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters. Via various three-dimensional plots, curve plots, density plots and contour plots, dynamical characteristics of these waves are represented.