Abstract In this study, the bilinear formalism, bilinear Bäcklund transformations (BBT) and Lax pair of the stochastic potential Korteweg–De Vries equation (spKdV) are established using the Bell polynomial approach. The spKdV equation, found in applications related to electric circuits and multi-component plasmas, is utilized to characterize the weak dispersive effects on the transmission of photons and nonlinear optical solitons. Using the bilinear neural network method (BNNM), we obtain the analytical solutions of the spKdV and discuss the physical behavior of these solutions with various graphical representations. In addition, we obtain the conservation vectors of the model using the multiplier method. We expect that the findings will yield a profound understanding of the fundamental dynamics and characteristics of the model.
Ay et al. (Thu,) studied this question.