Exact Solutions and Qualitative Analysis of the Stochastic Model for Embedded Solitons with \(\chi ^{(2)}\) and \(\chi ^{(3)}\) Nonlinear Susceptibilities

IF 1.3 4区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

International Journal of Theoretical Physics Pub Date : 2024-10-01 DOI:10.1007/s10773-024-05793-7

Yu-Fei Chen

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引用次数: 0

Abstract

The exact solutions and qualitative analysis of the stochastic governing model for embedded solitons with \(\chi ^{(2)}\) and \(\chi ^{(3)}\) nonlinear susceptibilities are investigated in this study. The model introduces a stochastic term-white noise for the first time, bringing the model closer to reality. The trial equation method is used for mathematical analysis and the complete discriminant system for polynomial method is used for qualitative analysis. Using the bifurcation theory and the complete discriminant system for polynomial method, the existence of the soliton and periodic solutions is confirmed and the exact travelling wave solutions are generated to validate our findings. Furthermore, we explore the various sorts of exact solutions by illustrating the associated phase diagrams and providing two-dimensional diagrams to demonstrate the model’s dynamical behavior. The plethora of exact solutions shows that the effect of white noise exists only in the phase component of the solitons, providing insight into the optical solitons of stochastic nonlinear models.

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有\(\chi ^{(2)}\) 和\(\chi ^{(3)}\) 的嵌入孤子随机模型的精确解与定性分析非线性敏感性

本研究探讨了具有（\chi ^{(2)}\）和（\chi ^{(3)}\）非线性敏感性的嵌入孤子随机调控模型的精确解和定性分析。该模型首次引入了随机项--白噪声，使模型更接近现实。数学分析采用试验方程法，定性分析采用多项式完全判别系统法。利用分岔理论和多项式方法的完全判别式系统，证实了孤子解和周期解的存在，并生成了精确的行波解来验证我们的发现。此外，我们还通过说明相关相图来探索各种精确解，并提供二维图来展示模型的动力学行为。大量精确解表明，白噪声的影响只存在于孤子的相位分量中，这为随机非线性模型的光学孤子提供了启示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Theoretical Physics 物理-物理：综合

CiteScore

2.50

自引率

21.40%

发文量

258

审稿时长

3.3 months

期刊介绍： International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.