Solitons’ behavior of waves by the effect of linearity and velocity of the results of a model in magnetized plasma field

Abstract

The nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov model plays the behavior of weakly nonlinear ion-acoustic waves in a magnetized electron-positron plasma, containing the same capacity of cool and hot components of each species. In this article, we have investigated the mathematical model namely, (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation through the new auxiliary equation method for locating the closed-form travelling and solitary wave solutions. We have constructed a well-built 3D wave profile that signifies the variations in the same solution for particular values of the associated parameters. The novel point of this article is that, the generic values of the velocity parameter (λ) of the obtained solutions represent in the wave profile which thoroughly explains the reasons for the change in the variation of solitons. Besides, the type of wave profile subject to different values ​​of all other parameters that are related to the linearity of the stated model is also discussed. We have obtained numerous new wave solutions that establish the effectiveness of the implemented method in solving evolution equation which is nonlinear in nature and has higher dimension (HNEEs). These discussions may be useful or helpful in further research on this model. Besides, the implemented method is reliable for exploring important nonlinear waves that improve a variety of dynamic models arising in nonlinear science, mathematical physics, and engineering fields.