Investigation of Brownian motion in stochastic Schrödinger wave equation using the modified generalized Riccati equation mapping method

Abstract
This work investigates the stochastic nonlinear Schrödinger equation in a more extended form, influenced by multiplicative noise which represents the temporal change of fluctuations. To obtain novel optical soliton solutions, the nonlinear partial differential equation is transformed into a nonlinear ordinary differential equation via symmetry reduction (nonclassical symmetry). This stochastic nonlinear problem is proposed to be solved by using the modified generalized Riccati equation mapping method. The resulting stochastic solitons show how waves dispersion throughout transmissions via optical fibers. With the use\r\nof this method, we can investigate an expansive range of solutions from important physical standpoints, such as dark, bright, singular, and periodic solitons, as well as their noise term effects related to Brownian motion based on the Itô sense. Both 2D and 3D graphs are used to display the impact of the noise term on the solitons. The comes about and calculations show the importance, exactness, and effectiveness of the strategy. The model under consideration is also examined through the concept of modulation instability analysis. Different stable and unstable nonlinear stochastic differential equations that are found in mathematics,\r\nphysics, and other connected ranges can be solved by utilizing this technique. Furthermore, the bifurcation of phase portraits are studied.

Author
Dr. Karmina Ali

DOI
https://doi.org/10.1007/s11082-024-06865-y

Publisher
Optical and Quantum Electronics

ISSN
0306-8919

Publish Date: