In this article, we establish solitary wave solutions to the Estevez-Mansfield-Clarkson (EMC) equation and the coupled sine-Gordon equations which are model equations to analyze the formation of shapes in liquid drops, surfaces of negative constant curvature, etc. through contriving the generalized Kudryashov method. The extracted results introduce several types’ solitary waves, such as the kink soliton, bell-shape soliton, compacton, singular soliton, peakon and other sort of soliton for distinct valuation of the unknown parameters. The achieved analytic solutions are interpreted in details and their 2D and 3D graphs are sketched. The obtained solutions and the physical structures explain the soliton phenomenon and reproduce the dynamic properties of the front of the travelling wave deformation generated in the dispersive media. It shows that the generalized Kudryashov method is powerful, compatible and might be used in further works to found novel solutions for other types of nonlinear evolution equations ascending in physical science and engineering.

在本文中，我们建立了Estevez-Mansfield-Clarkson（EMC）方程和正弦-Gordon耦合方程（它们是模型方程）的孤立波解，以分析液滴中的形状，负曲率恒定的表面等的形成。设计广义的Kudryashov方法。提取的结果引入了几种类型的孤波，例如扭折孤子，钟形孤子，紧实子，奇异孤子，peakon和其他种类的孤子，用于未知参数的不同评估。将详细解释所获得的解析解决方案，并绘制其2D和3D图形。所获得的解和物理结构解释了孤子现象，并再现了在分散介质中产生的行波形变前沿的动态特性。