Study of W-shaped, V-shaped, and other type of surfaces of the ZK-BBM and GZD-BBM equations

The Zakharov-Kuznetsov Benjamin-Bona-Mahony equation and its generalized form, considered in this study are two notable models for describing the magneto-acoustic waves in plasma, acoustic-gravity waves, the acoustic waves in harmonic crystals, long-wavelength in liquids, hydro-magnetic waves, shallow water waves etc. The sine-Gordon expansion (SGE) approach is put to use to acquire the broad-spectral typical solitary wave solutions from the exact solutions and to establish new shape of surfaces, namely the W-shaped, V-shaped, parabolic, compacton, bright and dark soliton for specific parameter values. Different types of solitons in terms of hyperbolic, and trigonometric functions are achieved. We present three-dimensional, two-dimensional, and contour plots of the results obtained through setting different parametric values to objectify the facts modulated by the formerly acknowledged models by computerized software Matlab. The solutions achieved prove that the SGE approach is a powerful and effective technique in physical sciences and engineering for analyzing nonlinear evolutionary equations.

Automated summary

The study investigates the Zakharov-Kuznetsov Benjamin-Bona-Mahony equation and its generalized form using the sine-Gordon expansion approach to find various solitary wave solutions and establish new surface shapes. The results obtained through Matlab software demonstrate the effectiveness and power of the SGE method in analyzing nonlinear evolutionary equations in physical sciences and engineering.