Dynamic Behaviors of the Dark Higher Order Rogue Waves and Interaction Inductions of a (3 + 1)-Dimensional Model

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-26 DOI:10.1002/mma.10836

Na Cao, XiaoJun Yin, LiYang Xu, ChunXia Wang

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引用次数: 0

Abstract

The research obtained dark second-order rogue waves and two sets of interaction solutions for (3 + 1)-dimensional equation by using symbolic calculation and two induction formulas. The two sets of interaction solutions are about second-order rogue waves and multiple stripes, second-order rogue waves and multiple solitons. Six sets of composite diagrams are made to show the interactions in three dimensions. The second-order rogue waves merge from two low-amplitude tops into one high-amplitude top if they meet with multiple stripes, and the amplitude increases with the increase of stripes' number. The second-order rogue waves are usually generated in the center of two kinky solitons if they meet with multiple solitons, and the amplitude increases with the increase of solitons' number. No matter what kind of rendezvous, we see the energy transfer from solitons to rogue waves and back to solitons. This will be useful in studying the evolution of rogue wave.

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暗高阶异常波的动力学行为和（3 + 1）维模型的相互作用诱导

利用符号计算和两个归纳公式，得到了暗二阶异常波和（3 + 1）维方程的两组相互作用解。这两组相互作用解分别是二阶异常波和多条纹，二阶异常波和多孤子。制作了六组复合图，以三维方式显示相互作用。当二阶异常波遇到多个条纹时，从两个低振幅顶部合并为一个高振幅顶部，并且随着条纹数量的增加，振幅增加。二阶异常波通常在两个弯曲孤子的中心产生，当遇到多个孤子时，其振幅随孤子数的增加而增大。无论以何种方式会合，我们都能看到能量从孤子转移到异常波，再转移回孤子。这对研究异常浪的演化具有重要意义。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.