The main emphasis of this paper is on soliton studies incorporating differential group delay, where, for the first time, the Lakshmanan–Porsezian–Daniel equation is employed in the presence of white noise. The model’s soliton solutions are effectively recovered using a new mapping method. Therefore, a complete range of solitons is revealed, highlighting that the influence of white noise remains localized to the phase component of the solitons along both vectors.
- White noise
- Wiener process