{"title":"五阶非线性薛定谔方程中椭圆函数背景上的 W 形孤子、呼吸波和流氓波解决方案","authors":"Fang-Cheng Fan , Wei-Kang Xie","doi":"10.1016/j.wavemoti.2024.103334","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate a fifth-order nonlinear Schrödinger equation, which can be applied to describe the propagation of ultrashort pulses in optical fibers. We provide the eigenfunctions of the Lax pair associated with the elliptic function seed solutions cn and dn. Using the Darboux transformation method, the W-shaped solitons, breathers, periodic solutions and rogue waves on the elliptic functions cn and dn background are obtained, the corresponding dynamical properties and evolutions are illustrated graphically by choosing proper parameters, the variations for amplitudes and periods of these solutions are analyzed. The relationship between parameters and solutions’ structures is discussed. To the best of our knowledge, the W-shaped solitons on the elliptic function background are presented for the first time. The results in this paper might be useful for us to understand some characteristics and relations of breathers and rogue waves on the elliptic functions cn and dn background in various physical equations with higher-order effects.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"129 ","pages":"Article 103334"},"PeriodicalIF":2.1000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"W-shaped soliton, breather and rogue wave solutions on the elliptic function background in a fifth-order nonlinear Schrödinger equation\",\"authors\":\"Fang-Cheng Fan , Wei-Kang Xie\",\"doi\":\"10.1016/j.wavemoti.2024.103334\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we investigate a fifth-order nonlinear Schrödinger equation, which can be applied to describe the propagation of ultrashort pulses in optical fibers. We provide the eigenfunctions of the Lax pair associated with the elliptic function seed solutions cn and dn. Using the Darboux transformation method, the W-shaped solitons, breathers, periodic solutions and rogue waves on the elliptic functions cn and dn background are obtained, the corresponding dynamical properties and evolutions are illustrated graphically by choosing proper parameters, the variations for amplitudes and periods of these solutions are analyzed. The relationship between parameters and solutions’ structures is discussed. To the best of our knowledge, the W-shaped solitons on the elliptic function background are presented for the first time. The results in this paper might be useful for us to understand some characteristics and relations of breathers and rogue waves on the elliptic functions cn and dn background in various physical equations with higher-order effects.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"129 \",\"pages\":\"Article 103334\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wave Motion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165212524000647\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524000647","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了五阶非线性薛定谔方程,该方程可用于描述超短脉冲在光纤中的传播。我们提供了与椭圆函数种子解 cn 和 dn 相关的 Lax 对的特征函数。利用达布变换方法,得到了椭圆函数 cn 和 dn 背景上的 W 形孤子、呼吸子、周期解和流氓波,并通过选择适当的参数,以图解的方式说明了相应的动力学性质和演变,分析了这些解的振幅和周期变化。讨论了参数与解的结构之间的关系。据我们所知,本文首次提出了椭圆函数背景上的 W 形孤子。本文的结果可能有助于我们理解各种物理方程中具有高阶效应的椭圆函数 cn 和 dn 背景上的呼吸波和流氓波的一些特征和关系。
W-shaped soliton, breather and rogue wave solutions on the elliptic function background in a fifth-order nonlinear Schrödinger equation
In this paper, we investigate a fifth-order nonlinear Schrödinger equation, which can be applied to describe the propagation of ultrashort pulses in optical fibers. We provide the eigenfunctions of the Lax pair associated with the elliptic function seed solutions cn and dn. Using the Darboux transformation method, the W-shaped solitons, breathers, periodic solutions and rogue waves on the elliptic functions cn and dn background are obtained, the corresponding dynamical properties and evolutions are illustrated graphically by choosing proper parameters, the variations for amplitudes and periods of these solutions are analyzed. The relationship between parameters and solutions’ structures is discussed. To the best of our knowledge, the W-shaped solitons on the elliptic function background are presented for the first time. The results in this paper might be useful for us to understand some characteristics and relations of breathers and rogue waves on the elliptic functions cn and dn background in various physical equations with higher-order effects.
期刊介绍:
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.