{"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}
引用次数: 0
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.
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