Solitonic behaviors in the coupled Drinfeld-Sokolov-Wilson system with fractional dynamics

I investigated soliton phenomena in a prominent nonlinear fractional partial differential equation (FPDE) namely the conformable coupled Drinfeld-Sokolov-Wilson system (CCDSWS) using a novel variant of the novel extended direct algebraic method (EDAM), namely $r$+mEDAM. The conformable fractional derivatives are used to generalize the model due to the memory and hereditary features that are inherent in the fractional dynamics. The model was initially transformed into a more manageable system of integer-order nonlinear ordinary differential equations (NODEs) through the implementation of complex transformation. The obtained system of NODEs is further transformed into a system of algebraic equations, which yields, by solving new plethora of soliton solutions for CCDSWS in the form of generalized trigonometrical, exponential hyperbolical, and rational functions. Moreover, we employed 2D, 3D, and contour graphics to show the behavior of acquired solitons, making it abundantly evident that the obtained solitons take the shape of kink, anti-kink, bright, dark, bright-dark, and bell-shaped kink solitons within the framework of CCDSWS. The results confirmed the efficiency of the presented approach in finding solitonic solutions, which in its turn expands knowledge of nonlinear FPDEs. The aimed to theoretical and application perspectives in fractional solitons applicable in areas such fluid mechanics, plasma physic, optical communications, etc.