{"title":"(3+1)维正弦-戈登方程一些精确解的动力学特性","authors":"Jiaming Guo, Maohua Li","doi":"10.1016/j.wavemoti.2024.103354","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional sine-Gordon equation is systematically investigated. Firstly, the integrability of the equation is demonstrated by Painlevé analysis. Secondly, based on the Hirota bilinear method, the <span><math><mi>N</mi></math></span>-soliton solution of the <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional sine-Gordon equation is derived. Then, by selecting and establishing conjugate relationships between parameters, the kink solutions, the breather solutions and their hybrid solutions were obtained. Finally, the lump solutions of equation are derived by selecting appropriate functions in the solution. In addition, the dynamic behavior of these solutions is systematically analyzed by their respective density profile plots and three-dimensional diagrams.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"130 ","pages":"Article 103354"},"PeriodicalIF":2.1000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The dynamics of some exact solutions to a (3+1)-dimensional sine-Gordon equation\",\"authors\":\"Jiaming Guo, Maohua Li\",\"doi\":\"10.1016/j.wavemoti.2024.103354\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, a <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional sine-Gordon equation is systematically investigated. Firstly, the integrability of the equation is demonstrated by Painlevé analysis. Secondly, based on the Hirota bilinear method, the <span><math><mi>N</mi></math></span>-soliton solution of the <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional sine-Gordon equation is derived. Then, by selecting and establishing conjugate relationships between parameters, the kink solutions, the breather solutions and their hybrid solutions were obtained. Finally, the lump solutions of equation are derived by selecting appropriate functions in the solution. In addition, the dynamic behavior of these solutions is systematically analyzed by their respective density profile plots and three-dimensional diagrams.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"130 \",\"pages\":\"Article 103354\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-06-05\",\"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/S0165212524000842\",\"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/S0165212524000842","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}
The dynamics of some exact solutions to a (3+1)-dimensional sine-Gordon equation
In this paper, a -dimensional sine-Gordon equation is systematically investigated. Firstly, the integrability of the equation is demonstrated by Painlevé analysis. Secondly, based on the Hirota bilinear method, the -soliton solution of the -dimensional sine-Gordon equation is derived. Then, by selecting and establishing conjugate relationships between parameters, the kink solutions, the breather solutions and their hybrid solutions were obtained. Finally, the lump solutions of equation are derived by selecting appropriate functions in the solution. In addition, the dynamic behavior of these solutions is systematically analyzed by their respective density profile plots and three-dimensional diagrams.
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.
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