{"title":"钟摆型方程绝热极限的类wkb方法","authors":"Andrey V. Ivanov","doi":"10.1109/DD.2000.902355","DOIUrl":null,"url":null,"abstract":"We consider the ordinary differential equation of the second order x/spl uml/+/spl psi/(/spl epsi/t) sin(x-/spl phi/(/spl epsi/t))=0 with the coefficients /spl psi/ and /spl phi/ depending slowly on time. By using a Wentzel-Kramers-Brillouin (WKB)-like method we construct two asymptotic series for a general solution of the equation in the limit /spl epsi//spl rarr/0 (adiabatic limit). One of them is true when the variable t is far from the zeroes of the coefficient /spl psi/ and the other one is valid in the neighborhoods of these these zeroes.","PeriodicalId":184684,"journal":{"name":"International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"WKB-like method for the adiabatic limit of a pendulum type equation\",\"authors\":\"Andrey V. Ivanov\",\"doi\":\"10.1109/DD.2000.902355\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the ordinary differential equation of the second order x/spl uml/+/spl psi/(/spl epsi/t) sin(x-/spl phi/(/spl epsi/t))=0 with the coefficients /spl psi/ and /spl phi/ depending slowly on time. By using a Wentzel-Kramers-Brillouin (WKB)-like method we construct two asymptotic series for a general solution of the equation in the limit /spl epsi//spl rarr/0 (adiabatic limit). One of them is true when the variable t is far from the zeroes of the coefficient /spl psi/ and the other one is valid in the neighborhoods of these these zeroes.\",\"PeriodicalId\":184684,\"journal\":{\"name\":\"International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450)\",\"volume\":\"28 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DD.2000.902355\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DD.2000.902355","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
WKB-like method for the adiabatic limit of a pendulum type equation
We consider the ordinary differential equation of the second order x/spl uml/+/spl psi/(/spl epsi/t) sin(x-/spl phi/(/spl epsi/t))=0 with the coefficients /spl psi/ and /spl phi/ depending slowly on time. By using a Wentzel-Kramers-Brillouin (WKB)-like method we construct two asymptotic series for a general solution of the equation in the limit /spl epsi//spl rarr/0 (adiabatic limit). One of them is true when the variable t is far from the zeroes of the coefficient /spl psi/ and the other one is valid in the neighborhoods of these these zeroes.
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