Some new soliton solutions to the (3 + 1)-dimensional generalized KdV-ZK equation via enhanced modified extended tanh-expansion approach

In this article, The (3 + 1)-dimensional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) which explains the influence of the magnetic field on the weak nonlinear ion-acoustic waves investigated in the field of plasma conjured up including both cold and hot electrons. GKdV-zk techniques solutions are obtained using the improved modified extended tanh expansion method, which is one of the most efficient algebraic methods for obtaining accurate solution to nonlinear partial differential equations. We aim to show how the analyzed model’s parameter impact soliton behavior by choosing different bright and single soliton forms and by developing various analytical optical soliton solutions for the explored equation. Methodology: In order to apply the suggested method, we used a complex wave transform to derive the nonlinear ordinary differential form of the analyzed equation. Then, using the method, we were able to obtain the polynomial form, leading to a set of linear equations. The conclusion of solving the linear equations problem, the outcomes of the analyzed model, and the suggested strategy are all included in different solution sets. After choosing the appropriate set from these sets, using the solution functions, and utilizing the wave transformation provided by the approach, we were able to arrive at the optical soliton solutions by providing the central equation. Finding: The proposed method has successfully produced a number of soliton solutions and several analytical optical solutions to such model. The research shows that the parameters of the model may have a variety of effects on the behavior of solitons, categories based on the soliton type. The findings we get in this article can be used to research and compare numerical and experimental data with analytical solving problems in plasma physics. Originality: This study differs from others in that it assessed the impact that parameters of the model have on the actions of solitons, despite the fact that the proposed technique was applied for the first time on the topic under investigation and numerous soliton types were created. This study focuses on the influence of model parameters on solitons behavior.