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آنالیز نیمه کلاسیک برای معادلات غیرخطی شرودینگر - تجزیه و تحلیل WKB، نقاط کانونی، حالت های منسجم
آنالیز نیمه کلاسیک برای معادلات غیرخطی شرودینگر - تجزیه و تحلیل WKB، نقاط کانونی، حالت های منسجم

Semi-Classical Analysis for Nonlinear Schrödinger Equations - WKB Analysis, Focal Points, Coherent States
نویسنده: Remi Carles
سال انتشار: 2021
تعداد صفحات: 367
زبان فایل: English
فرمت فایل: pdf
حجم فایل: 7MB
قیمت: 500,000ريال

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Publisher : World Scientific Publishing

ISBN-10 : 981122790X

ISBN-13 : 978-9811227905

ASIN : B08L941FKW

The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent. Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrödinger equations in negative order Sobolev spaces. The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.