Solitary wave solutions and investigation the effects of different wave velocities of the nonlinear modified Zakharov–Kuznetsov model for the wave propagation in nonlinear media

Abstract

The modified Zakharov-Kuznetsov (mZK) model convey a significant role to analyze the inner mechanism of physical compound phenomenon in the field of two-dimensional discrete electrical lattice, the electrical waves in cold plasmas, plasma physics, nonlinear optics, wave behaviors of deep oceans, etc. In this study, numerous new, advanced, and more general exact solitary travelling wave solutions are explored to the early stated nonlinear model by the aid of newly developed generalized exponential rational function (GERF) method through the traveling wave transformation. The established solutions are in terms of trigonometric functions, rational functions, hyperbolic functions, exponential rational functions, and complex-soliton solutions. The results reveal that the free parameters significantly influence the existence of traveling waves, as well as nature, shape, and stability. The established soliton solutions demonstrate that the method is effective, compatible, scientifically efficient and easily applicable to identify a variety of wave structures of nonlinear evolution models. The mathematical simulations of the results were conducted by sketching 3D and 2D structures for different values of the associated parameters by the aid of the Wolfram Mathematica program.