{"title":"Bäcklund变换的几何II: monge - ampantere不变量","authors":"Yuhao Hu","doi":"10.1093/integr/xyz011","DOIUrl":null,"url":null,"abstract":"\n This article is concerned with the question: For which pairs of hyperbolic Euler–Lagrange systems in the plane does there exist a rank-$1$ Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler–Lagrange systems. In addition, we discover a class of Bäcklund transformations relating two hyperbolic Euler–Lagrange systems of distinct types.","PeriodicalId":242196,"journal":{"name":"Journal of Integrable Systems","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Geometry of Bäcklund transformations II: Monge–Ampère invariants\",\"authors\":\"Yuhao Hu\",\"doi\":\"10.1093/integr/xyz011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n This article is concerned with the question: For which pairs of hyperbolic Euler–Lagrange systems in the plane does there exist a rank-$1$ Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler–Lagrange systems. In addition, we discover a class of Bäcklund transformations relating two hyperbolic Euler–Lagrange systems of distinct types.\",\"PeriodicalId\":242196,\"journal\":{\"name\":\"Journal of Integrable Systems\",\"volume\":\"39 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Integrable Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/integr/xyz011\",\"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 Integrable Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/integr/xyz011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Geometry of Bäcklund transformations II: Monge–Ampère invariants
This article is concerned with the question: For which pairs of hyperbolic Euler–Lagrange systems in the plane does there exist a rank-$1$ Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler–Lagrange systems. In addition, we discover a class of Bäcklund transformations relating two hyperbolic Euler–Lagrange systems of distinct types.
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