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A Dressing Method in Mathematical Physics: 28 (Mathematical Physics Studies, 28) - Tapa dura

Libro 4 de 24: Mathematical Physics Studies

Doktorov, Evgeny V.; Leble, Sergey B.

 
9781402061387: A Dressing Method in Mathematical Physics: 28 (Mathematical Physics Studies, 28)
Tapa dura
ISBN 10: 1402061382 ISBN 13: 9781402061387
Editorial: Springer, 2007

Sinopsis

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.

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De la contraportada

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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Editorial
Springer
Año de publicación
2007
Idioma
Inglés
ISBN 10 
1402061382
ISBN 13 
9781402061387
Encuadernación
Tapa dura
Número de páginas
412
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