Exact solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky system using Sardar sub-equation method

Abstract

In this paper, the new modification of the Sardar sub-equation method is used to generate a wide variety of exact solutions for the (2+1)-dimensional Konopelchenko-Dubrovsky system. We focus on investigating the Konopelchenko-Dubrovsky equation, which serves as a mathematical model for studying nonlinear waves in the field of mathematical physics. This equation specifically captures the behavior of waves with weak dispersion, allowing us to explore the intricate dynamics and characteristics associated with such wave phenomena. By delving into the properties and solutions of this system, we aim to deepen our understanding of nonlinear wave propagation and its implications in the broader field of mathematical physics. The exact solutions generated through this modified method provide valuable insights into the propagation and interaction of waves with weak dispersion in the system. The obtained novel solutions are expressed as hyperbolic, and trigonometric functions. The proposed model successfully constructs various types of solutions, including singular, dark, bright, trigonometric, periodic, dark-bright, exponential, and hyperbolic. These solutions are presented with appropriate parameter values in both 3D and 2D graphics.