Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Abstract

The improved modified extended tanh‐function approach was used to study optical stochastic soliton solutions and other exact stochastic solutions for the nonlinear Schrödinger‐Hirota equation with multiplicative white noise. The derived solutions include stochastic bright solitons, stochastic singular solitons, stochastic periodic solutions, stochastic singular periodic solutions, stochastic exponential solutions, stochastic rational solutions, and stochastic Jacobi elliptic doubly periodic solutions. Constraints on the parameters were taken into account to ensure the existence of the obtained stochastic soliton solutions. Additionally, selected solutions were presented graphically to illustrate the physical characteristics of the stochastic solutions. In this paper, we used Mathematica (11.3) packages to find the coefficients and Matlab (R2015a) packages to plot the graphs.

Novel highly dispersive soliton solutions in couplers for optical metamaterials: leveraging generalized Kudryashov’s Law of refractive index with eighth-order dispersion and multiplicative white noise

“…Finally, λ j , μ j , and θ j (with j = 1, 2) denote coefficients of self-steepening (SS) terms and nonlinear dispersion terms, respectively. The constant σ measures noise strength, with W(t) representing a standard Wiener process responsible for introducing stochastic fluctuations into the system [29][30][31][32][33][34][35][36][37].In these studies, the form of the Wiener process W(t), also known as a Brownian motion, can be described by the following characteristics:…”