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1. |
Record Nr. |
UNINA9910816776503321 |
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Autore |
Sakhnovich Alexander |
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Titolo |
Inverse problems and nonlinear evolution equations : solutions, Darboux matrices and Weyl-Titchmarsh functions / / by Alexander Sakhnovich, Lev Sakhnovich, Inna Roitberg |
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Pubbl/distr/stampa |
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Berlin ; ; Boston : , : Walter de Gruyter GmbH & Co., KG, , [2013] |
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©2013 |
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Descrizione fisica |
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1 online resource (356 p.) |
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Collana |
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De Gruyter Studies in Mathematics ; ; 47 |
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Altri autori (Persone) |
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RoitbergInna |
SakhnovichL. A |
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Disciplina |
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Soggetti |
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Boundary value problems |
Darboux transformations |
Evolution equations, Nonlinear |
Functions |
Inverse problems (Differential equations) |
Matrices |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographies and index. |
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Nota di contenuto |
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Front matter -- Preface -- Notation -- Contents -- 0 Introduction -- 1 Preliminaries -- 2 Self-adjoint Dirac system: rectangular matrix potentials -- 3 Skew-self-adjoint Dirac system: rectangular matrix potentials -- 4 Linear system auxiliary to the nonlinear optics equation -- 5 Discrete systems -- 6 Integrable nonlinear equations -- 7 General GBDT theorems and explicit solutions of nonlinear equations -- 8 Some further results on inverse problems and generalized Bäcklund-Darboux transformation (GBDT) -- 9 Sliding inverse problems for radial Dirac and Schrödinger equations -- Appendices -- A General-type canonical system: pseudospectral and Weyl functions -- B Mathematical system theory -- C Krein's system -- D Operator identities corresponding to inverse problems -- E Some basic theorems -- Bibliography -- Index |
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Sommario/riassunto |
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This book is based on the method of operator identities and related |
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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. |
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2. |
Record Nr. |
UNISA990002391680203316 |
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Autore |
VOLPE, Gioacchino |
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Titolo |
1. : [1815-1898] / Gioacchino Volpe |
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Pubbl/distr/stampa |
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Descrizione fisica |
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Collocazione |
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X.3.B. 1477/1a (ISP II 169/I) |
X.3.B. 1477/1 (III E 237/1) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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3. |
Record Nr. |
UNINA9910299991503321 |
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Titolo |
Algebra, Geometry and Mathematical Physics : AGMP, Mulhouse, France, October 2011 / / edited by Abdenacer Makhlouf, Eugen Paal, Sergei D. Silvestrov, Alexander Stolin |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2014 |
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ISBN |
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Edizione |
[1st ed. 2014.] |
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Descrizione fisica |
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1 online resource (680 p.) |
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Collana |
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Springer Proceedings in Mathematics & Statistics, , 2194-1017 ; ; 85 |
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Disciplina |
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Soggetti |
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Algebra |
Geometry, Differential |
Mathematical physics |
Nonassociative rings |
Topological groups |
Lie groups |
Engineering mathematics |
Engineering - Data processing |
Differential Geometry |
Theoretical, Mathematical and Computational Physics |
Non-associative Rings and Algebras |
Topological Groups and Lie Groups |
Mathematical and Computational Engineering Applications |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters and index. |
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Nota di contenuto |
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Part I Algebra -- Part II Geometry -- Part III Dynamical Symmetries and Conservation Laws -- Part IV Mathematical Physics and Applications. |
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Sommario/riassunto |
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This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers and advanced students. |
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