{"title":"(3+1)-dimensional generalized Kadomtsev-Petviashvili equation 的 Wronskian 解、双线性 Bäcklund 变换、准周期波和渐近行为","authors":"Caifeng Zhang, Zhonglong Zhao, Juan Yue","doi":"10.1016/j.wavemoti.2024.103327","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the integrability of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which is widely used in fluid mechanics and theoretical physics. The <span><math><mi>N</mi></math></span>-soliton solution is obtained via the Hirota’s bilinear method. The Wronskian solution is derived by using the Wronskian technique for the bilinear form. Through the exchange formula, we deduce the bilinear Bäcklund transformation consisting of four equations and six parameters. In order to consider the quasi-periodic wave having complex structure, one-, two- and three-periodic waves are investigated systemically by combining the Hirota’s bilinear method with Riemann theta function. Furthermore, the corresponding graphs of periodic wave are presented by considering the geometric properties between the characteristic lines. The propagation characteristics of periodic waves are investigated by virtue of the characteristic lines. Finally, the asymptotic relationships between quasi-periodic wave solutions and soliton solutions are established theoretically under a condition of the small amplitude limit. The analytical method used in this paper can be applied in other integrable systems.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"128 ","pages":"Article 103327"},"PeriodicalIF":2.1000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wronskian solutions, bilinear Bäcklund transformation, quasi-periodic waves and asymptotic behaviors for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation\",\"authors\":\"Caifeng Zhang, Zhonglong Zhao, Juan Yue\",\"doi\":\"10.1016/j.wavemoti.2024.103327\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we investigate the integrability of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which is widely used in fluid mechanics and theoretical physics. The <span><math><mi>N</mi></math></span>-soliton solution is obtained via the Hirota’s bilinear method. The Wronskian solution is derived by using the Wronskian technique for the bilinear form. Through the exchange formula, we deduce the bilinear Bäcklund transformation consisting of four equations and six parameters. In order to consider the quasi-periodic wave having complex structure, one-, two- and three-periodic waves are investigated systemically by combining the Hirota’s bilinear method with Riemann theta function. Furthermore, the corresponding graphs of periodic wave are presented by considering the geometric properties between the characteristic lines. The propagation characteristics of periodic waves are investigated by virtue of the characteristic lines. Finally, the asymptotic relationships between quasi-periodic wave solutions and soliton solutions are established theoretically under a condition of the small amplitude limit. The analytical method used in this paper can be applied in other integrable systems.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"128 \",\"pages\":\"Article 103327\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-04-16\",\"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/S016521252400057X\",\"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/S016521252400057X","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}
Wronskian solutions, bilinear Bäcklund transformation, quasi-periodic waves and asymptotic behaviors for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation
In this paper, we investigate the integrability of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which is widely used in fluid mechanics and theoretical physics. The -soliton solution is obtained via the Hirota’s bilinear method. The Wronskian solution is derived by using the Wronskian technique for the bilinear form. Through the exchange formula, we deduce the bilinear Bäcklund transformation consisting of four equations and six parameters. In order to consider the quasi-periodic wave having complex structure, one-, two- and three-periodic waves are investigated systemically by combining the Hirota’s bilinear method with Riemann theta function. Furthermore, the corresponding graphs of periodic wave are presented by considering the geometric properties between the characteristic lines. The propagation characteristics of periodic waves are investigated by virtue of the characteristic lines. Finally, the asymptotic relationships between quasi-periodic wave solutions and soliton solutions are established theoretically under a condition of the small amplitude limit. The analytical method used in this paper can be applied in other integrable systems.
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.