Multi-soliton, Rogue Wave and Periodic Wave Solutions of Generalized ($$2+1$$) Dimensional Boussinesq Equation

Abstract

In this work, we investigate a new generalized ($$2+1$$) dimensional Boussinesq Equation. This integrable shallow water wave equation is studied by virtue of the Simplified Hirota’s bilinear Method to derive single soliton, multi-soliton solutions and Extended Homoclinic Test Approach Method to derive rogue wave, multi-travelling wave and singular periodic wave solutions. The analytical solutions have different physical structures are graphically analyzed and demonstrated their dynamical behavior by means of two-dimensional, three-dimensional and contour plots.