Analytical solutions and stability of the resonant stochastic nonlinear Schrödinger equation under multiplicative perturbations

In this piece of research, the influence of multiplicative white noise on the nonlinear fluctuations of the stochastic nonlinear Schrödinger equation with resonance is investigated. By employing a phase-modulated transformation to incorporate stochastic effects, the governing equation is reduced to a stochastic nonlinear ordinary differential equation. Exact analytical solutions, including periodic and solitonic waveforms, are then constructed by means of the Improved F-expansion method and the [Formula: see text]-expansion technique. Through the separation of real and imaginary components, a detailed assessment of the impact of random fluctuations on amplitude variation, wave stability, and resonant energy exchange is carried out. A comparative analysis reveals that both methods successfully capture distinct solution structures across different parameter regimes. Explicit solutions under stochastic modulation are thereby provided, advancing the understanding of resonance-driven processes in nonlinear dispersive systems. The results are expected to be of value in diverse areas such as nonlinear optics, plasma physics, and quantum information processing, where stochastic influences are central to wave propagation and coherence. The dynamic nature and physical implications of the solutions have been illustrated using surface and line plots.