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.

本研究中考虑的 Zakharov-Kuznetsov Benjamin-Bona-Mahony 方程及其广义形式是描述等离子体中的磁声波、声引力波、谐波晶体中的声波、液体中的长波长的两个著名模型，水磁波，浅水波等。 正弦-戈登扩展（SGE）方法用于从精确解中获取广谱典型孤立波解并建立新的表面形状，即W-特定参数值的形状、V 形、抛物线、压实子、亮和暗孤子。实现了双曲函数和三角函数方面的不同类型的孤子。我们呈现三维、二维、以及通过设置不同参数值获得的结果的等高线图，以客观化由计算机软件 Matlab 先前公认的模型调制的事实。所获得的解决方案证明 SGE 方法是物理科学和工程中用于分析非线性演化方程的强大而有效的技术。