Stochastic resonant NLSE with cubic-quintic-septic-nonlocal nonlinearity: Soliton dynamics and noise-induced phenomena

This research examines the stochastic resonant nonlinear Schrödinger equation (NLSE) with cubic-quintic-septic nonlocal nonlinearity in the It ô framework, incorporating spatio-temporal dispersion (STD), inter-modal dispersion (IMD), resonant nonlinearities, and multiplicative white noise. Using Kudryashov’s method and the $P^6-$model expansion approach, novel families of bright, dark, singular, Jacobi-elliptic, and periodic stochastic solitons are derived, with exact constraint conditions ensuring physical validity. Numerical simulations reveal noise-induced amplitude modulation, phase jitter, rogue-wave-like spikes, and stochastic resonance phenomena that transition periodic backgrounds into emergent soliton structures. These findings demonstrate multiplicative noise’s dual role in destabilizing conventional solitons while generating resonance-enhanced coherent waveforms, filling the gap in unified models combining higher-order nonlinearities, nonlocality, and stochasticity. The numerical results were obtained using the split-step Fourier method to validate the analytical findings. The results advance soliton theory for realistic optical fibers, photonic lattices, metamaterials, and plasma systems, enabling noise-robust signal transmission and nonlinear wave control.