A Dressing Method in Mathematical Physics
Language: English
Published by Springer Netherlands, 2010
- Softcover
- New
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Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Unifying concept for solving linear and nonlinear equations of mathematical physicsCurrent status os research in the fieldThis monograph systematically develops and considers the so-called dressing method for solving differential equa.
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- Title
- A Dressing Method in Mathematical Physics
- Author
- Evgeny V. Doktorov|Sergey B. Leble
- Publisher
- Springer Netherlands
- Publication year
- 2010
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 9048175488
- ISBN 13
- 9789048175482
- Series
- Book 4 of 24: Mathematical Physics Studies
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. 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.
"Synopsis" may belong to another edition of this title.
From the Back Cover
The monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation from (maybe trivial) solution of the same or related equation. 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, the Riemann-Hilbert problem in the form proposed by Shabat and Zakharov for soliton equations and its extension in terms of the d-bar formalism comprise the main objects of the book. Throughout the text, a generally sufficient "linear experience" of readers is exploited, with a special attention 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. An extension of the classical Darboux transformations to nonlinear equations in 1+1 and 2+1 dimensions, as well as its factorization are discussed in detail. The applicability of the local and non-local Riemann-Hilbert problem-based approach and its generalization in terms of the d-bar method are illustrated on various nonlinear equations.
"About the title" may belong to another edition of this title.
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