CNLS-p方程及其退化孤子解的研究
Study on CNLS-p Equation and Its Degenerate Soliton Solutions
DOI: 10.12677/PM.2023.136158, PDF,   
作者: 叶 艳, 张和颜：浙江师范大学数学科学学院，浙江 金华
关键词: Darboux变换；模平方分解；孤子解；Darboux Transformation； The Decomposition of the Modulus Square； Soliton Solutions
摘要: 本文基于Darboux变换研究了CNLS-p方程，得到了一些位于零背景上的精确解，如孤子解、退化孤子解等。特别地，我们用数学软件绘制出了相应解的图像，并进行了动力学行为分析。此外，基于模平方的分解讨论了二阶退化孤子解的渐近形式，并展示了其近似轨道。
Abstract: In this paper, we study the CNLS-p equation based on the Darboux transformation, and obtain some exact solutions under the zero background condition, such as soliton solutions, degenerate soliton solutions, etc. Especially, we use mathematical software to draw the image of the corresponding solutions to analyze the dynamic behaviors. In addition, we discuss the asymptotic forms of the second-order degenerate soliton solutions by using the decomposition of the modulus square, and show their approximate orbits.
文章引用：叶艳, 张和颜. CNLS-p方程及其退化孤子解的研究[J]. 理论数学, 2023, 13(6): 1565-1570. https://doi.org/10.12677/PM.2023.136158

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