{"title":"(2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani 方程的非线性波和转换机制","authors":"Xueqing Zhang, Bo Ren","doi":"10.1016/j.wavemoti.2024.103383","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, state transition waves are investigated in a (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation by analyzing characteristic lines. Firstly, the <span><math><mi>N</mi></math></span>-soliton solutions are given by using the Hirota bilinear method. The breather and lump waves are constructed by applying complex conjugation limits and the long-wave limit method to the parameters. In addition, the transition condition of breather and lump wave are obtained by using characteristic line analysis. The state transition waves consist of quasi-anti-dark soliton, M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, W-shaped soliton, and quasi-periodic wave soliton. Through analysis, when solitary wave and periodic wave components undergo nonlinear superposition, it leads to the formation of breather waves and transformed wave structures. It can be used to explain the deformable collisions of transformation waves after collision. Furthermore, the time-varying property of transformed waves are studied using characteristic line analysis. Based on the high-order breather solutions, the interactions involving breathers, state transition waves, and solitons are exhibited. Finally, the dynamics of these hybrid solutions are analyzed through symbolic computations and graphical representations.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"130 ","pages":"Article 103383"},"PeriodicalIF":2.1000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear waves and transitions mechanisms for (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation\",\"authors\":\"Xueqing Zhang, Bo Ren\",\"doi\":\"10.1016/j.wavemoti.2024.103383\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, state transition waves are investigated in a (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation by analyzing characteristic lines. Firstly, the <span><math><mi>N</mi></math></span>-soliton solutions are given by using the Hirota bilinear method. The breather and lump waves are constructed by applying complex conjugation limits and the long-wave limit method to the parameters. In addition, the transition condition of breather and lump wave are obtained by using characteristic line analysis. The state transition waves consist of quasi-anti-dark soliton, M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, W-shaped soliton, and quasi-periodic wave soliton. Through analysis, when solitary wave and periodic wave components undergo nonlinear superposition, it leads to the formation of breather waves and transformed wave structures. It can be used to explain the deformable collisions of transformation waves after collision. Furthermore, the time-varying property of transformed waves are studied using characteristic line analysis. Based on the high-order breather solutions, the interactions involving breathers, state transition waves, and solitons are exhibited. Finally, the dynamics of these hybrid solutions are analyzed through symbolic computations and graphical representations.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"130 \",\"pages\":\"Article 103383\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-05\",\"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/S0165212524001136\",\"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/S0165212524001136","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
本文通过分析特征线研究了 (2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani 方程中的状态转换波。首先,利用 Hirota 双线性方法给出了 N 个oliton 解。通过对参数应用复共轭极限和长波极限方法,构建了呼吸波和块状波。此外,还利用特征线分析法得到了呼吸波和块波的过渡条件。状态转换波包括准反暗孤子、M 形孤子、振荡 M 形孤子、多峰孤子、W 形孤子和准周期波孤子。通过分析,当孤波和周期波成分发生非线性叠加时,会形成呼吸波和变换波结构。它可以用来解释变换波碰撞后的可变形碰撞。此外,还利用特征线分析法研究了变换波的时变特性。基于高阶呼吸解,展示了涉及呼吸波、状态转换波和孤子的相互作用。最后,通过符号计算和图形表示分析了这些混合解的动力学。
Nonlinear waves and transitions mechanisms for (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation
In this paper, state transition waves are investigated in a (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation by analyzing characteristic lines. Firstly, the -soliton solutions are given by using the Hirota bilinear method. The breather and lump waves are constructed by applying complex conjugation limits and the long-wave limit method to the parameters. In addition, the transition condition of breather and lump wave are obtained by using characteristic line analysis. The state transition waves consist of quasi-anti-dark soliton, M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, W-shaped soliton, and quasi-periodic wave soliton. Through analysis, when solitary wave and periodic wave components undergo nonlinear superposition, it leads to the formation of breather waves and transformed wave structures. It can be used to explain the deformable collisions of transformation waves after collision. Furthermore, the time-varying property of transformed waves are studied using characteristic line analysis. Based on the high-order breather solutions, the interactions involving breathers, state transition waves, and solitons are exhibited. Finally, the dynamics of these hybrid solutions are analyzed through symbolic computations and graphical representations.
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.