Noise effects on soliton structures of nonlinear Schrödinger equation with generalized Kudryashov's law non-linearity using modified extended mapping technique.

The main objective of this research is to extend and analyze a stochastic form of the resonant nonlinear Schrödinger equation (NLSE) that incorporates spatio-temporal dispersion, intermodal dispersion, and multiplicative white noise in the Itô sense, together with a generalized Kudryashov-type nonlinearity. By employing the modified extended mapping technique (MEMT), the study aims to derive a broad class of exact analytical solutions, including bright, dark, and singular solitons, as well as periodic, singular periodic, hyperbolic, rational, Jacobi elliptic, and Weierstrass elliptic waveforms. Furthermore, it seeks to investigate the influence of stochastic perturbations on soliton amplitude and phase. The research also provides two- and three-dimensional graphical simulations to validate the analytical results and to illustrate the dynamic features of the obtained solutions. Compared with previous MEMT-based studies, the novelty of this work lies in addressing the stochastic version of the resonant NLSE with higher-order nonlinearities and dispersion effects, thereby uncovering new families of solutions and clarifying their robustness under noise. Overall, the work not only develops a comprehensive mathematical framework for handling nonlinear stochastic systems but also offers practical insights into noise-resistant soliton transmission with potential applications in optical communications, plasma physics, and nanophotonics.