In our current article, we establish four new types of group for the optical soliton solutions to the three dimensional modified Zakharov–Kuznetsov equation’s new model. Four distinct and impressive techniques are used for this target, which are the extended simple equation method (ESEM), the extended direct algebraic method (EDAM), the ( GG′ )— expansion method and the Paul-Painleve approach method (PPAM). The four suggested techniques are discovered recently to derive the exact solutions for many other NLPDE that arising in various branches of science and usually give good results. These techniques have been used for the first time to extract the soliton solutions of this model. The four employed methods are applied serially and in the same time. Our solutions weren’t achieved previously via any other authors who applied any other methods.