Inverse Problems and Nonlinear Evolution Equations
Language: English
Published by De Gruyter Jul 2013, 2013
- Hardcover
- New
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.
AbeBooks seller since January 11, 2012
Condition: New
£ 128.03
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This item is printed on demand - it takes 3-4 days longer - Neuware -This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund-Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses. 356 pp. Englisch.…
Seller Inventory # 9783110258608
- Title
- Inverse Problems and Nonlinear Evolution Equations
- Author
- Inna Ya. Roitberg
- Publisher
- De Gruyter Jul 2013
- Publication year
- 2013
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 3110258609
- ISBN 13
- 9783110258608
- Item weight
- 856 grams
- Dimensions
- 246x175x31 mm
- Series
- Book 36 of 60: De Gruyter Studies in Mathematics
This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role.
The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way.
The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas.
The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
"Synopsis" may belong to another edition of this title.
About the Author
Alexander L. Sakhnovich, University of Vienna, Austria; Lev A. Sakhnovich, Milford, Connecticut, USA; Inna Ya. Roitberg, Universität Leipzig, Germany.
"About the title" may belong to another edition of this title.
BuchWeltWeit Ludwig Meier e.K.
Bergisch Gladbach, Germany
AbeBooks seller since January 11, 2012
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