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OverviewThis monograph systematically develops and considers the so-called 'dressing method' for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. The primary topics of the dressing method covered here are: the Moutard and Darboux transformations discovered in XIX century as applied to linear equations; the Backlund transformation in differential geometry of surfaces; the factorization method; and the Riemann-Hilbert problem in the form proposed by Shabat and Zakharov for soliton equations, plus its extension in terms of the d-bar formalism. Throughout, the text exploits the 'linear experience' of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions. Various linear equations of classical and quantum mechanics are solved by the Darboux and factorization methods. Full Product DetailsAuthor: Evgeny Doktorov , Sergey LeblePublisher: Springer Imprint: Springer ISBN: 9781280864247ISBN 10: 1280864249 Pages: 383 Publication Date: 01 January 2007 Audience: General/trade , General Format: Undefined Publisher's Status: Active Availability: In stock We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |