Construction of a weakly nonlinear dispersion solitary wave solution for the Zakharov–Kuznetsov-modified equal width dynamical equation

By applying the modification form of extended auxiliary equation mapping method, we investigated the solitary wave solutions of Zakharov–Kuznetsov-modified equal width dynamical equation. We obtained these solitary wave solutions in the form of bright and dark solitons, periodic solitary wave, traveling wave, trigonometric functions, elliptic functions and hyperbolic functions solutions. The physical structure of these new solutions showed two and three dimensions graphically by using the computer software Mathematica. The obtained new solutions are the power and effectiveness of this new method. We can solve other nonlinear system of PDEs, which are involved in mathematical physics and other various branches of physical sciences with the help of this new method.