Exploring Solitons and Modulation Instability in the Nonlinear Fractional Coupled Painlevé–Burgers Model

This work reveals the novel types of exact solitons for the coupled (2 + 1)-dimensional Painlevé’s–Burgers model in the sense of novel fractional derivative. To gain the different kinds of exact solitons, we utilized the modified extended direct algebraic technique. Dynamical behaviors of the achieved results are explained with the help of 2-dimensional, 3-dimensional, and contour plots. Furthermore, to confirm the stability of the concerned model and the obtained solutions, we utilized the stability and modulation instability analysis. The achieved results are newer than the existing results of the concerned equation. The gained results are useful in many areas, including fluid dynamics, nonlinear wave propagation, turbulence and chaos, plasma physics, traffic flow, weather forecasting, ocean engineering, aerodynamics, etc. At the end, it is concluded that the utilized technique is also helpful and applicable for the other nonlinear fractional equations in applied science and engineering.