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\begin{document}

\title{The new stochastic solutions to the perturbed NLSE}



\author[1]{Hesham Abdelwahed}%
\author[2]{mahmoud abdelrahman}%
\affil[1]{Mansoura University}%
\affil[2]{department of mathematics-faculty of science-mansoura university}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
This article extracts exact solutions for the perturbed nonlinear
Schr\selectlanguage{ngerman}ödinger's equation (PNLSE) with Kerr law nonlinearity forced by
multiplicative noise in It\^{}o sense by utilizing the unified solver
method. The presented solutions involve three types: rational function,
trigonometric function and hyperbolic function solutions. These
stochastic solutions may be applicable for investigation various complex
phenomena in applied science and new physics. We exhibit the influence
of multiplicative noise on the solution of the PNLSE forced by
multiplicative noise in It\^{}o sense. The study and acquired solutions
clarify that the unified solver technique is sturdy and efficient.
Finally, some 3D proles to some of the gained solutions are also
illustrated.%
\end{abstract}\selectlanguage{ngerman}%



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