On the analytical soliton-like solutions to (2+1)-dimensional fractional asymmetric Nizhnik-Novikov-Veselov system arising in incompressible fluids

Due to the numerous applications of the Nizhnik-Novikov-Veselov system (NNVS) in fluid mechanics, thus, the current investigation is focused on studying the fractional form of this model to reveal the ambiguity around many nonlinear phenomena that arise in different fluid medias. Accordingly, we aim to derive several families of symmetric solitons and traveling wave solutions to the (2 + 1)-dimensional fractional asymmetric NNVS (FANNVS), defined in conformable fractional derivatives’ sense. For this purpose, a groundbreaking analytical technique known as the modified extended direct algebraic method (mEDAM) is utilized to solve and analyze the FANNVS. According to this method, four cases with several families of soliton-like solutions are derived. Our research uncovers various soliton solutions, including solitary waves, periodic waves, shocks, dual shock waves (lump waves), and anti-shock waves. These solutions are graphically discussed to understand their dynamical proprieties against the fractional parameters. This broad range of soliton-like solutions supports the relevance of our findings and demonstrates the effectiveness of our methodology. These findings significantly advance the field by deepening our understanding of solitonic behavior in FANNVS and demonstrating the effectiveness of the medium approach in solving challenging nonlinear systems.