Dynamics of kink solitons under additive white noise in the power-law nonlinear Schrödinger equation

We investigate how additive spatio-temporal white noise affects kink solitons in the (1 + 1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity. We formulate the stochastic model, derive a deterministic baseline via a wave transformation and expectation analysis, and construct kink solutions for the noise-free limit. We then perform numerical simulations across noise intensities to quantify changes in soliton amplitude and phase. At low noise intensity, kink profiles remain stable and coherent over long times; increasing noise produces measurable shallowing, phase distortion, and loss of coherence, culminating in structural degradation at moderate levels. To contrast stochastic effects with deterministic perturbations, we examine a chaotic Nuclear Spin Generator (NSG) system as a case study, showing that chaos persists under noise while modulating the wave response. The results delineate parameter regimes in which kink solitons remain robust in power-law media and clarify how stochastic forcing alters propagation, with implications for applications in nonlinear optics, Bose-Einstein condensates, and spintronics.