Exploring soliton solutions of Zakharov–Kuznetsov dynamical model with applications

In this paper, we investigate the soliton solution of the Zakharov–Kuznetsov (Z–K) equation using a modified unified method. The Z–K equation pertains to the evolution of quasi- (1D) shallow-water waves under conditions, where viscosity and surface tension effects can be disregarded. By employing the newly modified unified method, we derive analytical solutions employing hyperbolic, trigonometric, rational, and exponential functions. Interestingly, several of these solutions are novel and have not been described earlier. These distinct wave solutions hold noteworthy applications in various fields, including applied sciences and engineering. By setting particular values for the solution parameters, we reveal new graphical patterns that escalate our interpretation of the physical behavior within this model. Computational efforts and outcomes underscore the potency and robustness of the suggested technique, suggesting its potential applicability to various nonlinear models appearing in mathematical physics and diverse scientific domains. Moreover, this technique can be utilized to solve other intricate Z–K equations in the field of mathematical physics.