{"title":"广义(3+1)维KdV方程的整体解、相互作用解和呼吸解","authors":"YU Minghui, WANG Yunhu","doi":"10.21656/1000-0887.430353","DOIUrl":null,"url":null,"abstract":"Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the \"fusion\" and \"fission\" phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained.","PeriodicalId":8341,"journal":{"name":"应用数学和力学","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lump Solutions, Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations\",\"authors\":\"YU Minghui, WANG Yunhu\",\"doi\":\"10.21656/1000-0887.430353\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the \\\"fusion\\\" and \\\"fission\\\" phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained.\",\"PeriodicalId\":8341,\"journal\":{\"name\":\"应用数学和力学\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"应用数学和力学\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21656/1000-0887.430353\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用数学和力学","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21656/1000-0887.430353","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Lump Solutions, Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations
Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the "fusion" and "fission" phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained.
期刊介绍：
Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.
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