The objective of this paper is to locate the embedded solitons with ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ nonlinear susceptibilities in presence of multiplicative noise. Itô Calculus was implemented to carry out the analysis of the corresponding stochastic differential equation. The unified Riccati equation expansion method and enhanced Kudryashov’s approach yielded dark, bright and singular solitons. The derived soliton solutions show that the effect of white noise is present only in the phase component.

中文翻译：

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具有 χ(2) 和 χ(3) 非线性磁化率的嵌入式孤子通过伊藤微积分具有乘法白噪声

本文的目的是定位嵌入的孤子${\chi }^{\left(2\right)}$和${\chi }^{\left(3\right)}$存在乘性噪声时的非线性敏感性。Itô Calculus 用于执行相应的随机微分方程的分析。统一的 Riccati 方程展开方法和增强的 Kudryashov 方法产生了暗、亮和奇异的孤子。导出的孤子解表明白噪声的影响仅存在于相位分量中。