Narrow Results

The main aim of this paper is to investigate the various dimensional nonlinear Fokas and Breaking soliton equations via a powerful analytical method, namely, sine-Gordon expansion method. Many new solutions such as complex combined dark-bright soliton solutions, singular and hyperbolic functions are derived. Choosing the suitable values of these parameters, various novel simulations are also plotted. Such results explain the wave behavior of the governing models, physically.

In the current study, we instigate the four-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation. The NLmZK equation guides the attitude of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Two different methods are used, namely the sine-Gordon expansion method (SGEM) and the $(1/G^{\prime })$-expansion method to the proposed model. We have successfully constructed some topological, non-topological, and wave solutions. In addition, the 2D, 3D, and contour graphs of the solutions are also plotted under the choice of appropriate values of the parameters.