A study of nonlinear extended Zakharov–Kuznetsov dynamical equation in (3+1)-dimensions: Abundant closed-form solutions and various dynamical shapes of solitons

Abstract

In this work, we execute the generalized exponential rational function (GERF) method to construct numerous and a large number of exact analytical solitary wave solutions of the nonlinear extended Zakharov–Kuznetsov (EZK) dynamical equation in (3+1)-dimensions. The implemented method is one of the best, most reliable, and efficient techniques in the present time for determining numerous closed-form wave analytic solutions to NPDEs. We have accomplished a variety of solitary wave solutions related to some arbitrary parameters under various family cases. These solutions take the following forms based on the free parameters chosen: exponential functions form, trigonometric functions form, and hyperbolic functions form. The obtained solutions are dissimilar and entirely new from the previous findings available in the literature. The dynamics of obtained solutions, namely, soltion, singular soliton wave, a periodic wave, bell-shape, anti-bell-shape wave, breather wave, and multisoliton wave solutions by the special-choice of parameters, are shown graphically in 3D, 2D, and corresponding density profiles. The results demonstrate that the employed computational strategy is efficient, direct, concise, and can be executed in various complex phenomena with symbolic computations. Furthermore, it is revealed that the generalized exponential rational function technique can be effectively utilized for several other NPDEs in engineering, sciences, and mathematical physics.