On the analysis and integrability of the time-fractional stochastic potential-KdV equation

This study investigates the invariance properties of the time-fractional stochastic potential-KdV (FSP-KdV) equation, intending to enhance our understanding of the dynamics associated with nonlinear photon and optical soliton propagation. The application of the Lie group analysis method enables the derivation of vector fields and symmetry reductions for the equation. Additionally, employing power series theory, the paper systematically constructs explicit power series solutions, offering a detailed derivation. The resulting wave propagation patterns of these solutions are depicted along the x-axis at various temporal instances. Finally, lever-aging a new conservation theorem, the study formulates two distinct conservation laws for the equation, presenting comprehensive and detailed derivations for each.