The Kawahara equation (KE) and the modified Kawahara equation (MKE) are important modeling equations to interpret shallow water waves with surface tension, magneto-acoustic wave in plasma and gravity waves. In this study, the stable broad-ranging soliton solutions including the well-known bell-shape soliton, anti-bell shape soliton, periodic soliton, compacton, kink, etc. are established through the sine-Gordon expansion (SGE) method. The effect of the physical parameters, namely the dispersion and perturbed dispersive coefficients in the surface elevation are shown through the figure. The surface elevations remain ascertainable for diverse values of the physical and the associated free parameters. The 3D and contour plot of the ascertained solutions clarifies the surface wave properties. The achieved results for each modeling equation provide a significant contribution in analyzing the ion-acoustic waves in plasma, gravity waves, the surface waves in shallow water. This study asserts that the SGE method is reliable, competent, easy and powerful for extracting closed form soliton solutions.

Kawahara 方程 (KE) 和修正的 Kawahara 方程 (MKE) 是解释具有表面张力的浅水波、等离子体中的磁声波和重力波的重要建模方程。本研究通过正弦-戈登展开(SGE)方法建立了广为人知的钟形孤子、反钟形孤子、周期孤子、compacton、kink等稳定宽范围孤子解。物理参数的影响，即地表高程中的色散和摄动色散系数通过该图显示。对于物理参数和相关自由参数的不同值，表面高度仍然是可确定的。确定解的 3D 和等高线图阐明了表面波特性。每个建模方程所获得的结果为分析等离子体中的离子声波、重力波、浅水中的表面波提供了重要的贡献。本研究断言，SGE 方法对于提取封闭形式的孤子解决方案是可靠、有效、简单且强大的。