Chun-Yi Zhang, Yi-Tian Gao, Xiang-Hua Meng, Juan Li, Tao Xu, Guangmei Wei, Hong-Wu Zhu
{"title":"玻色-爱因斯坦凝聚体和流体动力学的变系数Korteweg-de Vries模型的可积性","authors":"Chun-Yi Zhang, Yi-Tian Gao, Xiang-Hua Meng, Juan Li, Tao Xu, Guangmei Wei, Hong-Wu Zhu","doi":"10.1088/0305-4470/39/46/008","DOIUrl":null,"url":null,"abstract":"The phenomena of the trapped Bose–Einstein condensates related to matter waves and nonlinear atom optics can be governed by a variable-coefficient Korteweg–de Vries (vc-KdV) model with additional terms contributed from the inhomogeneity in the axial direction and the strong transverse confinement of the condensate, and such a model can also be used to describe the water waves propagating in a channel with an uneven bottom and/or deformed walls. In this paper, with the help of symbolic computation, the bilinear form for the vc-KdV model is obtained and some exact solitonic solutions including the N-solitonic solution in explicit form are derived through the extended Hirota method. We also derive the auto-Bäcklund transformation, nonlinear superposition formula, Lax pairs and conservation laws of this model. Finally, the integrability of the variable-coefficient model and the characteristic of the nonlinear superposition formula are discussed.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":"{\"title\":\"Integrable properties of a variable-coefficient Korteweg–de Vries model from Bose–Einstein condensates and fluid dynamics\",\"authors\":\"Chun-Yi Zhang, Yi-Tian Gao, Xiang-Hua Meng, Juan Li, Tao Xu, Guangmei Wei, Hong-Wu Zhu\",\"doi\":\"10.1088/0305-4470/39/46/008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The phenomena of the trapped Bose–Einstein condensates related to matter waves and nonlinear atom optics can be governed by a variable-coefficient Korteweg–de Vries (vc-KdV) model with additional terms contributed from the inhomogeneity in the axial direction and the strong transverse confinement of the condensate, and such a model can also be used to describe the water waves propagating in a channel with an uneven bottom and/or deformed walls. In this paper, with the help of symbolic computation, the bilinear form for the vc-KdV model is obtained and some exact solitonic solutions including the N-solitonic solution in explicit form are derived through the extended Hirota method. We also derive the auto-Bäcklund transformation, nonlinear superposition formula, Lax pairs and conservation laws of this model. Finally, the integrability of the variable-coefficient model and the characteristic of the nonlinear superposition formula are discussed.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"29\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/46/008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/46/008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Integrable properties of a variable-coefficient Korteweg–de Vries model from Bose–Einstein condensates and fluid dynamics
The phenomena of the trapped Bose–Einstein condensates related to matter waves and nonlinear atom optics can be governed by a variable-coefficient Korteweg–de Vries (vc-KdV) model with additional terms contributed from the inhomogeneity in the axial direction and the strong transverse confinement of the condensate, and such a model can also be used to describe the water waves propagating in a channel with an uneven bottom and/or deformed walls. In this paper, with the help of symbolic computation, the bilinear form for the vc-KdV model is obtained and some exact solitonic solutions including the N-solitonic solution in explicit form are derived through the extended Hirota method. We also derive the auto-Bäcklund transformation, nonlinear superposition formula, Lax pairs and conservation laws of this model. Finally, the integrability of the variable-coefficient model and the characteristic of the nonlinear superposition formula are discussed.