BIFURCATING LUMP SOLITON STRUCTURES IN THE FRACTIONAL DRINFEL’D SOKOLOV WILSON FRAMEWORK

This research studies the space-time fractional wave circulation in shallow water mechanics through the construction of dynamic traveling wave solutions. It also highlights how fractional-order derivatives are critical in modeling complex wave concepts. Employing both the Riccati–Bernoulli sub-ODE technique and the Bäcklund transformation, we obtain several exact solutions in the form of lump, kink-type lump and Peregrine lump solutions. The solution profiles are then illustrated using 3D and 2D graphical representations to study the impact of the fractional-order parameter ([Formula: see text]) on the process of wave transmission and evolution. It aids the theoretical understanding of wave dynamics by exhibiting how the fractional-order parameters affect the nonlinear wave structures. The implications of these findings for applied mathematics and engineering include offering insights on fractional wave models to enhance refinement of numerical simulations. Thus, this work contributes significantly to mathematical physics concerning new ideas of fractional dynamics in nonlinear wave and its applications.