Diverse wave solutions to the new extended (2 + 1)-dimensional nonlinear evolution equation: Phase portrait, bifurcation and sensitivity analysis, chaotic pattern, variational principle, and Hamiltonian

The purpose of this work is to give a deeper exploration into the nonlinear dynamics of the new extended [Formula: see text]-dimensional nonlinear evolution equation (NEE) for oceanic wave. Wielding the semi-inverse method (SIM) and traveling wave transformation, we establish the variational principle (VP). On basis of the VP, the corresponding system’s Hamiltonian is extracted. Aided by the Galilean transformation, the planar dynamical system is obtained. Then the phase portraits are plotted and the bifurcation analysis is presented to discuss the existing conditions of the wave solutions. In addition, the chaotic behaviors and sensitivity analysis of the system are also elaborated via adding the perturbed term and taking the different initial conditions, respectively. In the end, two robust methods, the variational method that stemmed from the VP and Ritz method, as well as the Hamiltonian-based method are used to develop the diverse wave solutions, which include the bell-shaped solitary, anti-bell-shaped solitary and periodic wave solutions. The findings of this study are all novel and can enable us to gain a deeper understanding of the nonlinear dynamics of the equation being studied.