Novel stochastic embedded solitons with quadratic nonlinear susceptibility in the presence of multiplicative noise

Abstract

Abstract This paper addresses the modeling of optical systems with stochastic quadratic nonlinearity for the first time, a novel and challenging research area within nonlinear optics. By incorporating multiplicative white noise and quadratic nonlinear susceptibility, the study presents an innovative approach to recovering optical solutions. Leveraging the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo accent="false">′</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:mfrac> </mml:mstyle> </mml:math> -expansion method and extended Kudryashov’s method, new stochastic exact solutions are derived, encompassing bright, dark, singular, and trigonometric solitons. Graphical representations aid in understanding these solutions’ characteristics. Insights into the stochastic nature of optical solutions under various conditions are provided, offering valuable contributions to nonlinear optics and potential applications in telecommunications and materials science.