Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics

Abstract

We examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also in the construction of connections between the hydrodynamic and optical model fields. Moreover, unlike the Kadomtsev–Petviashvili equation (KPE), the KP-B equation allows the modeling of waves traveling in both directions and does not require the zero-mass assumption, which is necessary for many scientific applications. Considering these properties enables researchers to obtain more precise results in many physics and engineering applications, especially in research on the dynamics of water waves. We used the modified extended tanh function method (METFM) and Kudryashov’s method, which are easily applicable, do not require further mathematical manipulations, and give effective results to investigate the physical properties of the KP-B equation and its soliton solutions. As the output of the work, we obtained some new singular soliton solutions to the governed equation and simulated them with 3D and 2D graphs for the reader to understand clearly. These results and graphs describe the single and singular soliton properties of the (3+1)-dimensional KP-B equation that have not been studied and presented in the literature before, and the methods can also help in obtaining the solution to the evolution equations and understanding wave propagation in water wave dynamics.

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

“…In this section, we investigate Eq. ( 3 ) using bifurcation theory and phase portrait analysis 35 . The system described by Eq.…”

“…The Boussinesq model was initially established by Joseph Boussinesq in 1872 to explain how long, small-amplitude waves flow at a constant pace in a water channel with a constant depth. Additionally; the Boussinesq model is extensively applied in marine and coastal engineerings 35 . Because the Boussinesq model accurately models viscous flows involving various fluids with interfaces between them, the authors have considered it.…”