Solitons interaction and Turbulence in the Framework of Time Fractional Korteweg-de Vries Equation

As part of this study, we looked into the multi-soliton answers to the time fractional Korteweg-de Vries (TFKdV) equation using the simple and algebraic Hirota bilinear method (HBM). We have calculated the first four momentums of this evolution equation (TFKdV). The whole fractional derivatives are determined in the Caputo sense. We have graphically described the physical interpretation of the TFKdV equation's solution. Here, we also discussed the difference between the two-soliton interaction of exact solitons and time fractional solitons for the TFKdV equation using a graphical approach. We derive two soliton structures from the TFKdV equation and find that a certain value of the time fractional parameter converts the two soliton structures into a single soliton structure. Our investigations illustrate this previously undiscovered characteristic. We have depicted the effect of the fractional parameter on soliton turbulence through the derivation of third and fourth integral moments. We observe that the time fraction derivative during soliton turbulence significantly alters the soliton interaction and integral moments in the dominant interaction region of two-solitons.