Concatenation model: having the parabolic law in the presence of chromatic and spatio-temporal dispersion and investigation of multiplicative white noise effect via Itô calculus

Abstract This manuscript focuses on the stochastic optical soliton solution of the concatenation model having the parabolic law with chromatic and spatio-temporal dispersions. This model characterizes the propagation of optical pulses or wave packets through media where nonlinear dispersion, higher-order effects, and stochastic influences interact, significantly shaping the system’s dynamics. The “concatenation” concept refers to the combination of several nonlinear equations, including the nonlinear Schrödinger, Sasa–Satsuma, and Lakshmanan–Porsezian–Daniel equations, to capture a wide range of physical phenomena. The main equation is transformed using a wave transformation, reducing it to a nonlinear ordinary differential equation. This process simplifies the original equation, enabling a clearer comprehension of the underlying dynamics of the system. Thus, we retrieve the analytical solutions of the proposed equation utilizing the addendum to Kudryashov’s method and the Kudryashov auxiliary equation approach. Additionally, through the implementation of robust analytical methods, we systematically derive an extensive variety of soliton solutions including bright, W-shaped like, and kink solitons. Moreover, we investigate the noise effect on the dynamics of solitons.