Overview

"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."

Full Product Details

Author:   Evgeny V. Doktorov ,  Sergey B. Leble
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 2007
Volume:   28
Dimensions:   Width: 15.50cm , Height: 2.10cm , Length: 23.50cm
Weight:   0.629kg
ISBN:  

9789048175482

ISBN 10:   9048175488
Pages:   383
Publication Date:   25 November 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

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.

Reviews

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 Schrodinger 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)

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 Schroedinger 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)

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 Schroedinger 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)

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 Schrodinger 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)

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