{"title":"wadati - kono - ichiawa - shimizu (WKIS)方程的精确平稳解方法","authors":"R. A. Gorder","doi":"10.1143/PTP.128.993","DOIUrl":null,"url":null,"abstract":"We consider a method of obtaining exact implicit relations governing stationary solutions to the Wadati-Konno-Ichikawa-Shimizu (WKIS) equation. After a suitable transform, we put the WKIS equation into the form of a nonlinear ordinary differential equation. This equation has exact first and second integrals of motion. From this second integral, the exact equation governing the stationary solution to the WKIS equation is obtained. This relation may easily be inverted and plotted, to give the exact solution profiles. Furthermore, an exact formula for the period of oscillation in terms of the model parameters is obtained. Subject Index: 010, 030","PeriodicalId":49658,"journal":{"name":"Progress of Theoretical Physics","volume":"128 1","pages":"993-999"},"PeriodicalIF":0.0000,"publicationDate":"2012-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTP.128.993","citationCount":"8","resultStr":"{\"title\":\"Exact Stationary Solution Method for the Wadati-Konno-Ichikawa-Shimizu (WKIS) Equation\",\"authors\":\"R. A. Gorder\",\"doi\":\"10.1143/PTP.128.993\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a method of obtaining exact implicit relations governing stationary solutions to the Wadati-Konno-Ichikawa-Shimizu (WKIS) equation. After a suitable transform, we put the WKIS equation into the form of a nonlinear ordinary differential equation. This equation has exact first and second integrals of motion. From this second integral, the exact equation governing the stationary solution to the WKIS equation is obtained. This relation may easily be inverted and plotted, to give the exact solution profiles. Furthermore, an exact formula for the period of oscillation in terms of the model parameters is obtained. Subject Index: 010, 030\",\"PeriodicalId\":49658,\"journal\":{\"name\":\"Progress of Theoretical Physics\",\"volume\":\"128 1\",\"pages\":\"993-999\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1143/PTP.128.993\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Progress of Theoretical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1143/PTP.128.993\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress of Theoretical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1143/PTP.128.993","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exact Stationary Solution Method for the Wadati-Konno-Ichikawa-Shimizu (WKIS) Equation
We consider a method of obtaining exact implicit relations governing stationary solutions to the Wadati-Konno-Ichikawa-Shimizu (WKIS) equation. After a suitable transform, we put the WKIS equation into the form of a nonlinear ordinary differential equation. This equation has exact first and second integrals of motion. From this second integral, the exact equation governing the stationary solution to the WKIS equation is obtained. This relation may easily be inverted and plotted, to give the exact solution profiles. Furthermore, an exact formula for the period of oscillation in terms of the model parameters is obtained. Subject Index: 010, 030
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