Stochastic higher-order Lakshmanan–Porsezian–Daniel model with cubic-quintic law nonlinearities in the presence of spatio-temporal and chromatic dispersion terms

This work focuses on deriving optical soliton solutions for the stochastic variant of the higher-order Lakshmanan–Porsezian–Daniel (LPD) model, which incorporates cubic-quintic law nonlinearities alongside chromatic and spatio-temporal dispersion terms. The primary approach chosen for this purpose is the new Kudryashov method (nKM). Initially, bright and dark soliton solutions are derived. The stability of these dark and bright solitons is then verified using the Vakhitov–Kolokolov criterion. Subsequently, the impact of the stochastic term on the bright and dark solitons is examined. As an additional aspect, an investigation has been conducted on the effects of the model parameters, namely, group velocity dispersion and spatio-temporal dispersion terms.