Abstract
We are interested in studying some qualitative analysis and wave propagation and their applications to the Konopelchenko-Dubrovsky equation.Using the qualitative theory of planar systems and a complete discriminant system, we propose a new method. The proposed method is more efficient because it only creates real bounded wave solutions, which are desirable in real-world applications, as well as it is applicable to large classes of nonlinear partial differential equations. We present an algorithm for the proposed method to facilitate and clarify its applicability. Some new solutions are introduced using this method, and they are classified as periodic and solitary wave solutions. These solutions are graphically represented by displaying 3D and 2D graphic representations, as well as the contour plot. Furthermore, we investigate the impact of the included parameters on the obtained solutions. We numerically examine the 2D and 3D phase portraits after permitting a certain periodic additional term to arise, revealing the existence of quasi-periodic behavior.