AI 中文总结
本文研究广义非线性流体方程的可积性，采用可积方法获得孤波解并辅以模拟，通过分岔与稳定性分析建立了分析材料能量传播非线性响应的可靠框架。
AI 中文摘要
本文研究了兼具空间和时间演化的广义非线性流体方程的可积性特性。该非线性模型被公认为是用于表征光纤、金属离子流体等致密材料非线性动力学特性的可积工具，已广泛应用于电磁在受扰带电等离子体中传播的物理解释。本文采用多种可积方法，结合深入的解析分析，获得了广泛的孤波解；这些结果辅以计算模拟，加深了对能量准确图像流的理解。我们还对正则坐标进行了分岔分析，以研究参数变化对所考虑系统非线性行为的影响。随后，我们开展稳定性分析，评估光学孤子在平衡点附近特征的鲁棒性。这些结果为通过改变与该非线性方程模型相关的物理参数，分析材料用于能量传播的非线性响应，建立了可靠且准确的框架。
英文摘要
In this article, we explore the integrable aspects of generalized non-linear fluid equation possessing mixed spatial and time evolutions. This non-linear model has been acknowledged as integrable tool for the non-linear dynamical character- ization of dense material such as in optical fibre, metallic ionic fluid. This model widely has been applied in physical interpretations of electromagnetic propaga- tion through perturbed charged plasma. Here, we use few integrable approaches and attain a broad range of solitary solutions involve deep analytical analysis. These results are furnished with computational simulations, which enrich under- standing about the accurate pictorial flow of energy. We also present a bifurcation analysis for canonical coordinates to examine the impact of parameter variations on non-linear behavior of the systems under consideration. Subsequently, we per- form stability analysis to evaluate the robustness of optical solitons features in the vicinity of equilibrium points. These results establish the reliable and accurate framework for analyzing non linear response of materials for energy propagation by varying physical parameters associated with this non-linear equation model.
