{"title":"七阶KdV方程的扩展复解法亚纯解和Painlev?分析","authors":"Guoqiang Dang","doi":"10.2306/scienceasia1513-1874.2023.133","DOIUrl":null,"url":null,"abstract":": Using the traveling wave transformation, the seventh-order KdV equation reduces to a sixth-order complex differential equation (CDE), and we first prove that all meromorphic solutions of the CDE belong to the class W via Nevanlinna’s value distribution theory. Then abundant new meromorphic solutions of the sixth-order CDE have been established in the finite complex plane with the aid of an extended complex method and Painlevé analysis, which contains Weierstrass elliptic function solutions and exponential function solutions, some of them are whole new solutions comparing to the opening literature. We give the computer simulations of some elliptic and exponential solutions. At last, we investigate the meromorphic solutions of the nonlinear dispersive Kawahara equation as an application.","PeriodicalId":21577,"journal":{"name":"Scienceasia","volume":"33 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Meromorphic solutions of the seventh-order KdV equation by using an extended complex method and Painlev? analysis\",\"authors\":\"Guoqiang Dang\",\"doi\":\"10.2306/scienceasia1513-1874.2023.133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": Using the traveling wave transformation, the seventh-order KdV equation reduces to a sixth-order complex differential equation (CDE), and we first prove that all meromorphic solutions of the CDE belong to the class W via Nevanlinna’s value distribution theory. Then abundant new meromorphic solutions of the sixth-order CDE have been established in the finite complex plane with the aid of an extended complex method and Painlevé analysis, which contains Weierstrass elliptic function solutions and exponential function solutions, some of them are whole new solutions comparing to the opening literature. We give the computer simulations of some elliptic and exponential solutions. At last, we investigate the meromorphic solutions of the nonlinear dispersive Kawahara equation as an application.\",\"PeriodicalId\":21577,\"journal\":{\"name\":\"Scienceasia\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Scienceasia\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://doi.org/10.2306/scienceasia1513-1874.2023.133\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scienceasia","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.2306/scienceasia1513-1874.2023.133","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Meromorphic solutions of the seventh-order KdV equation by using an extended complex method and Painlev? analysis
: Using the traveling wave transformation, the seventh-order KdV equation reduces to a sixth-order complex differential equation (CDE), and we first prove that all meromorphic solutions of the CDE belong to the class W via Nevanlinna’s value distribution theory. Then abundant new meromorphic solutions of the sixth-order CDE have been established in the finite complex plane with the aid of an extended complex method and Painlevé analysis, which contains Weierstrass elliptic function solutions and exponential function solutions, some of them are whole new solutions comparing to the opening literature. We give the computer simulations of some elliptic and exponential solutions. At last, we investigate the meromorphic solutions of the nonlinear dispersive Kawahara equation as an application.
期刊介绍：
ScienceAsia is a multidisciplinary journal publishing papers of high quality bimonthly, in printed and electronic versions, by the Science Society of Thailand under Royal Patronage and the National Research Council of Thailand. The journal publishes original research papers that provide novel findings and important contribution to broad area in science and mathematics. Areas covered include Biological Sciences and Biotechnology, Chemistry and Material Sciences, Environmental and Applied Sciences, and Mathematics and Physical Sciences. Manuscripts may report scientifically useful data, observations or model predictions, and/or provide a new scientific concept or a new explanation of published results. Submissions of materials of current scientific interest are highly welcome, provided that there is sufficient scientific merit. The journal will not accept manuscripts which have been published or are being considered for publication elsewhere, nor should manuscripts being considered by ScienceAsia be submitted to other journals. Submitted manuscripts must conform to the guidelines given in the Instructions for Authors
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