A computational scheme and its comparison with optical soliton solutions for the stochastic Chen–Lee–Liu equation with sensitivity analysis

Abstract

In this study, the stochastic Chen–Lee–Liu equation is considered numerically and analytically which is forced by the multiplicative noise in the Itô sense. The Chen–Lee–Liu equation is a special type of Schrödinger’s equation which has applications in optical fibers and photonic crystal fibers. The stochastic Crank–Nicolson scheme is formed to obtain the computational results. The numerical scheme is analyzed under the mean square sense and Von-Neumann criteria to show consistence and stability, respectively. Meanwhile, stochastic optical soliton solutions are attained by using two techniques, namely, the modified auxiliary equation method and the generalized projective Riccati equation method. These methods provide us with the different types of optical soliton solutions such as hyperbolic, trigonometric, mixed trigonometric, and rational forms. Mainly, the comparison of computational results with newly constructed optical soliton solution is shown graphically. To compare these results, initial conditions and boundary conditions are constructed by selecting some soliton solutions. The 3D and line graphs are drawn by choosing different values of parameters. Additionally, the sensitivity analysis is observed for the different initial values.