New exact solutions of (3+1)-dimensional modified KdV-Zakharov-Kuznetsov equation by Sardar-subequation method

New solitary wave solutions are developed for various shapes of three-dimensional nonlinear partial differential equations using the Sardar-Subequation method. Some periodic solitary wave solutions, including bright, dark, dark-bright, and singular periodic soliton solutions, are obtained. These solutions have broad applications in a particular category of applied sciences and physics. Graphical representations of the obtained results have been created using Maple 18 software to illustrate the accuracy and simplicity of the proposed method. Two-dimensional (2-D), three-dimensional (3-D), and 2-D contour plots have been used to depict the physical behavior of the observed patterns by incorporating relevant parameters. To demonstrate the robustness, sustainability, capability, and effectiveness of the present method, we have applied it to solve the nonlinear (3+1)-dimensional modified KdV-Zakharov-Kuznetsov equation.