Lump, soliton, and breather solutions of a (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation: theoretical investigation, bifurcation, quasiperiodic behavior and sensitivity analysis

The new extended (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation is investigated in this work. Through a dependent variable transformation, the model is transformed into Hirota's bilinear form. A variety of ansätze are incorporated to retrieve several exact solutions, such as lumps, periodic solutions, solitons, breathers, and various other interaction solutions. The physical attributes of the yielded solutions are highlighted in 3D and density plots. The parametric constraints and existence conditions are also studied. On the qualitative forefront, the model is investigated by the corresponding planar dynamical system. The dynamical system is then used for a comprehensive bifurcation and phase portrait analysis. The quasi-periodicity of the system is investigated through different chaos detection tools such as Poincaré maps, phase portraits, Lyapunov exponents, power spectrum, and time series analysis. The sensitivity of the system is explored through sensitivity analysis.