{"product_id":"9784431557012","title":"SpringerBriefs in Mathematical Physics","description":"\u003ch1\u003eSpringerBriefs in Mathematical Physics\u003c\/h1\u003e \u003ch2\u003eHonda, Naofumi; Kawai, Takahiro; Takei, Yoshitsugu\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels.\u003c\/p\u003e\u003cp\u003eAs M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the \u003ci\u003eJournal of Mathematical Physics\u003c\/i\u003e indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2015-07-21\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9784431557012\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-4-431-55702-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 126\u003c\/p\u003e ","brand":"Springer Japan","offers":[{"title":"Default Title","offer_id":46547627835532,"sku":"9784431557012","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9784431557012.jpg?v=1775835667","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9784431557012","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}