Analyzing the impact of white noise on optical solitons and various wave solutions in the stochastic fourth-order nonlinear Schrödinger equation

We derive novel soliton solutions and additional wave solutions for the stochastic nonlinear Schrödinger equation with fourth-order perturbations. The study employs an enhanced modified extended tanh-function approach that provides many solution types. These solutions comprise singular, bright, and...

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Bibliographic Details
Published in:Alexandria engineering journal Vol. 127; pp. 1049 - 1063
Main Authors: Shehab, Mohammed F., Ahmed, Hamdy M., Boulaaras, Salah, Osman, M.S., Ahmed, Karim K.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.08.2025
Elsevier
Subjects:
Improved modified extended tanh-function method
Partial differential equations
Solitons
Stochastic system
Wiener process
Wiener process
Improved modified extended tanh-function method
Partial differential equations
Stochastic system
Solitons
ISSN:1110-0168
Online Access:Get full text
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Summary:We derive novel soliton solutions and additional wave solutions for the stochastic nonlinear Schrödinger equation with fourth-order perturbations. The study employs an enhanced modified extended tanh-function approach that provides many solution types. These solutions comprise singular, bright, and dark solitons. Furthermore, solutions for Jacobi elliptic functions, Weierstrass elliptic functions, hyperbolic solutions, periodic solutions, and singular periodic solutions are established. This approach provides a useful and efficient way to find accurate stochastic solutions for a range of nonlinear stochastic partial differential equations. A significant gap in the current theoretical approaches is filled by the analysis, which guarantees a comprehensive and non-redundant base of solutions. The impact of the noise is illustrated graphically using examples of the recovered solutions with varying noise levels. The optical solitons produced in respect to this form have never been explored by the proposed technique before, and the results have never been published.
ISSN:1110-0168
DOI:10.1016/j.aej.2025.06.040