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|a 9781402061400
|9 978-1-4020-6140-0
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|a 10.1007/1-4020-6140-4
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|a Doktorov, Evgeny V.
|e author.
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|a A Dressing Method in Mathematical Physics
|h [electronic resource] /
|c by Evgeny V. Doktorov, Sergey B. Leble.
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| 264 |
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|a Dordrecht :
|b Springer Netherlands,
|c 2007.
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| 300 |
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|a XXIV, 383 p.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
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|a text file
|b PDF
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|a Mathematical Physics Studies ;
|v 28
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|a Mathematical preliminaries -- Factorization and classical Darboux transformations -- From elementary to twofold elementary Darboux transformation -- Dressing chain equations -- Dressing in 2+1 dimensions -- Applications of dressing to linear problems -- Important links -- Dressing via local Riemann–Hilbert problem -- Dressing via nonlocal Riemann–Hilbert problem -- Generating solutions via ? problem.
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|a 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.
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| 650 |
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|a Physics.
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| 650 |
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|a Nonassociative rings.
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| 650 |
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|a Rings (Algebra).
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| 650 |
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|a Functions of complex variables.
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| 650 |
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|a Applied mathematics.
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|a Engineering mathematics.
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|a Optics.
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| 650 |
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|a Electrodynamics.
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|a Physics.
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| 650 |
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|a Optics and Electrodynamics.
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| 650 |
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|a Appl.Mathematics/Computational Methods of Engineering.
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| 650 |
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|a Applications of Mathematics.
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| 650 |
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|a Mathematical Methods in Physics.
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| 650 |
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|a Non-associative Rings and Algebras.
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| 650 |
2 |
4 |
|a Functions of a Complex Variable.
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| 700 |
1 |
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|a Leble, Sergey B.
|e author.
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
0 |
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|t Springer eBooks
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| 776 |
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|i Printed edition:
|z 9781402061387
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| 830 |
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|a Mathematical Physics Studies ;
|v 28
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| 856 |
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|u http://dx.doi.org/10.1007/1-4020-6140-4
|z Full Text via HEAL-Link
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| 912 |
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|a ZDB-2-PHA
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| 950 |
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|a Physics and Astronomy (Springer-11651)
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