Soliton solutions and stability analysis of the stochastic nonlinear reaction-diffusion equation with multiplicative white noise in soliton dynamics and optical physics

In this article, we explored the stochastic nonlinear reaction-diffusion (RD) equation under the influence of multiplicative white noise. To obtain novel soliton solutions, we employed two powerful analytical techniques: the unified Riccati equation expansion method and the modified Kudryashov method. These methods yield a diverse set of soliton solutions, including combo-dark solitons, dark solitons, singular solitons, combo-bright-singular solitons, and periodic wave solutions. We also performed a comprehensive stability analysis of the stochastic nonlinear RD equation with multiplicative white noise. The findings provide valuable insights into the behavior of solitons in stochastic nonlinear systems, with significant implications for fields such as mathematical physics, nonlinear science, and applied mathematics. These results hold particular relevance for soliton dynamics in optical physics, where they can be applied to improve understanding of wave propagation in noisy environments, signal transmission, and the design of robust optical communication systems.