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Dressing Method in Mathematical Physics

Name: Dressing Method in Mathematical Physics
Brand: Springer-Verlag New York Inc.
SKU: 01417296
Price: 39520 HUF
Availability: InStock
Author: Evgeny V. Doktorov
ISBN: 9781402061387

Evgeny V. Doktorov

Sergey B. Leble

Language

English

Book Hardback

Libristo code: 01417296

Publishers Springer-Verlag New York Inc., May 2007

This monograph systematically develops and considers the so-called "dressing method" for solving dif... Full description

Libristo code: 01417296

271 b

39 520 Ft

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This 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 Bäcklund 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.