Analytical study of optical soliton solutions for a (2+1)-nonlinear coupled Konopelchenko-Dubrovsky equation in the tropical and mid-latitude tropospheres

Abstract This research work investigates the analytical soliton solution of $(2+1)$-dimensions of the Konopelchenko-Dubrovsky (KD) equation which depicts the nonlinear waves in mathematical physics with weak dispersion. The $(2+1)$-dimensional KD equation significantly enhances the discipline of atmospheric science by examining the characteristics of nonlinear wave phenomena, elucidating the intricate scattering effects and prolonged range interactions prevalent in tropical and mid-latitude atmospheric regions. This mathematical formulation yields a profound understanding of the interaction between equatorial and mid-latitude Rossby waves, effectively capturing their intricate dynamics and interrelations. We used the newly developed schemes known as the generalized Arnous and the $\exp(-\Theta(\mathcal{G}))$-expansion methods to find the analytical soliton solutions. Consequently, various novel collections of solutions, trigonometric, hyperbolic, rational, and logarithmic solutions, are identified. From these methodologies, we derive the kink and anti-kink soliton solutions. The kink soliton pertains to localized alterations in the curvature, amplitude, and morphology of the wave. This particular category of soliton signifies the existence of a pronounced transition between disparate wave height configurations. To gain a deeper understanding of the physical characteristics of these solutions, we present them with various visual representations such as 3D, 2D, contour, and density graphs. These methods have larger applicability and are useful for the $(2+1)$-dimensional KD equation expressing nonlinear physical models in the realm of nonlinear sciences rather than just the equation itself.