Evgeny V. Doktorov, Sergey B. Leble

A Dressing Method in Mathematical Physics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 383
• Erscheinungstermin: 19. Mai 2007
• Englisch
• ISBN-13: 9781402061400
• Artikelnr.: 37341075

Autorenporträt

Evgeny Doktorov, Institute of Physics, Minsk, Belarus / Sergey Leble, University of Technology, Gdansk, Poland

Inhaltsangabe

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.

Rezensionen

From the reviews: "This book is a collection of the work of the two authors over many years. ... The authors connect nicely the newest contributions and the 150 years of history of Darboux transformations and solvable potentials of the linear Schrödinger equation. ... The book can be recommended to graduate students ... ." (Dmitry E. Pelinovsky, Mathematical Reviews, Issue 2008 k) "The term 'dressing' generally implies a construction that contains a transformation from a simpler state to a more advanced state of a system. ... It provides new insight into this significant research area of great importance. ... The book can be of very great use to graduate students and professional mathematicians and physicists. ... It provides a good introduction to the dressing method, and it is definitely a good job." (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1142, 2008)