Probing nonlinear wave dynamics: Insights from the (2+1)-dimensional Konopelchenko-Dubrovsky System

The (2 + 1)-dimensional Konopelchenko-Dubrovsky system contributes to the field of atmospheric science by investigating the behaviour of nonlinear waves, revealing subtle scattering effects and extended-range interactions within the tropical and mid-latitude troposphere. This equation provides insights into the interplay between equatorial and mid-latitude Rossby waves, capturing their complex interactions and dynamics. Nonlinear waves are significant in atmospheric processes and understanding their dynamics is important for comprehending weather patterns. This study centres around the utilisation of the simplest equation method and extended hyperbolic function method to analyse these waves and derives many solutions that illustrate different wave patterns and behaviours intrinsic to the governed system. The simplest equation method enables the derivation of kink and multi-soliton solutions. This method allows for the extraction of solutions characterised by multiple solitary waves propagating without distortion. On the other hand, the extended hyperbolic function method provides anti-bell-shaped, periodic, and singular solutions. These diverse solution types portray various wave patterns and behaviours intrinsic to the equation under study. Additionally, 3D and 2D graphical representations are generated to visually depict the obtained solutions. Hence, this study not only contributes to the comprehension of non-linear wave dynamics in atmospheric science but also imparts knowledge on the broader applicability of mathematical methods in uncovering the underlying intricacies of natural phenomena in different fields of non-linear sciences.