Inverse Problems and Nonlinear Evolution Equations: Solutions, Darboux Matrices and Weyl-Titchmarsh Functions
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin
De Gruyter
2013
|
| Series: | De Gruyter studies in mathematics
|
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | 7.2 GBDT for linear system depending rationally on z Print version record |
| Physical Description: | 1 online resource (356 pages) |
| ISBN: | 3110258617 9783110258615 |
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MARC
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| 245 | 1 | 0 | |a Inverse Problems and Nonlinear Evolution Equations |b Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| 264 | 1 | |a Berlin |b De Gruyter |c 2013 | |
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| 500 | |a 7.2 GBDT for linear system depending rationally on z | ||
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| 505 | 8 | |a Preface; Notation; 0 Introduction; 1 Preliminaries; 1.1 Simple transformations and examples; 1.1.1 Dirac-type systems as a subclass of canonical systems; 1.1.2 Schrödinger systems as a subclass of canonical systems; 1.1.3 Gauge transformations of the Dirac systems; 1.2 S-nodes and Weyl functions; 1.2.1 Elementary properties of S-nodes; 1.2.2 Continual factorization; 1.2.3 Canonical systems and representation of the S-nodes; 1.2.4 Asymptotics of the Weyl functions, a special case; 1.2.5 Factorization of the operators S; 1.2.6 Weyl functions of Dirac and Schrödinger systems | |
| 505 | 8 | |a 2 Self-adjoint Dirac system: rectangular matrix potentials2.1 Square matrix potentials: spectral and Weyl theories; 2.1.1 Spectral and Weyl functions: direct problem; 2.1.2 Spectral and Weyl functions: inverse problem; 2.2 Weyl theory for Dirac system with a rectangularmatrix potential; 2.2.1 Direct problem; 2.2.2 Direct and inverse problems: explicit solutions; 2.3 Recovery of the Dirac system: general case; 2.3.1 Representation of the fundamental solution; 2.3.2 Weyl function: high energy asymptotics; 2.3.3 Inverse problem and Borg-Marchenko-type uniqueness theorem | |
| 505 | 8 | |a 2.3.4 Weyl function and positivity of S3 Skew-self-adjoint Dirac system: rectangular matrix potentials; 3.1 Direct problem; 3.2 The inverse problem on a finite interval and semiaxis; 3.3 System with a locally bounded potential; 4 Linear system auxiliary to the nonlinear optics equation; 4.1 Direct and inverse problems; 4.1.1 Bounded potentials; 4.1.2 Locally bounded potentials; 4.1.3 Weyl functions; 4.1.4 Some generalizations; 4.2 Conditions on the potential and asymptotics of generalized Weyl (GW) functions; 4.2.1 Preliminaries. Beals-Coifman asymptotics | |
| 505 | 8 | |a 4.2.2 Inverse problem and Borg-Marchenko-type result4.3 Direct and inverse problems: explicit solutions; 5 Discretesystems; 5.1 Discrete self-adjoint Dirac system; 5.1.1 Dirac system and Szegö recurrence; 5.1.2 Weyl theory: direct problems; 5.1.3 Weyl theory: inverse problems; 5.2 Discrete skew-self-adjoint Dirac system; 5.3 GBDT for the discrete skew-self-adjoint Dirac system; 5.3.1 Main results; 5.3.2 The fundamental solution; 5.3.3 Weyl functions: direct and inverse problems; 5.3.4 Isotropic Heisenberg magnet; 6 Integrable nonlinear equations | |
| 505 | 8 | |a 6.1 Compatibility condition and factorization formula6.1.1 Main results; 6.1.2 Proof of Theorem 6.1; 6.1.3 Application to the matrix "focusing" modified Korteweg-de Vries (mKdV); 6.1.4 Second harmonic generation: Goursat problem; 6.2 Sine-Gordon theory in a semistrip; 6.2.1 Complex sine-Gordon equation: evolution of the Weyl function and uniqueness of the solution; 6.2.2 Sine-Gordon equation in a semistrip; 6.2.3 Unbounded solutions in the quarter-plane; 7 General GBDT theorems and explicit solutions of nonlinear equations; 7.1 Explicit solutions of the nonlinear optics equation | |
| 505 | 8 | |a This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich. The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field | |
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 7 | |a Boundary value problems |2 fast | |
| 650 | 7 | |a Darboux transformations |2 fast | |
| 650 | 7 | |a Evolution equations, Nonlinear |2 fast | |
| 650 | 7 | |a Functions |2 fast | |
| 650 | 7 | |a Inverse problems (Differential equations) |2 fast | |
| 650 | 7 | |a Matrices |2 fast | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 4 | |a Evolution equations, Nonlinear | |
| 650 | 4 | |a Darboux transformations | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Functions | |
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| 700 | 1 | |a Sakhnovich, Alexander L. |e Sonstige |4 oth | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Sakhnovich, Lev A |t . Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
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Record in the Search Index
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| any_adam_object | |
| author | Sakhnovich, Lev A. |
| author_facet | Sakhnovich, Lev A. |
| author_role | aut |
| author_sort | Sakhnovich, Lev A. |
| author_variant | l a s la las |
| building | Verbundindex |
| bvnumber | BV043037065 |
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| contents | Preface; Notation; 0 Introduction; 1 Preliminaries; 1.1 Simple transformations and examples; 1.1.1 Dirac-type systems as a subclass of canonical systems; 1.1.2 Schrödinger systems as a subclass of canonical systems; 1.1.3 Gauge transformations of the Dirac systems; 1.2 S-nodes and Weyl functions; 1.2.1 Elementary properties of S-nodes; 1.2.2 Continual factorization; 1.2.3 Canonical systems and representation of the S-nodes; 1.2.4 Asymptotics of the Weyl functions, a special case; 1.2.5 Factorization of the operators S; 1.2.6 Weyl functions of Dirac and Schrödinger systems 2 Self-adjoint Dirac system: rectangular matrix potentials2.1 Square matrix potentials: spectral and Weyl theories; 2.1.1 Spectral and Weyl functions: direct problem; 2.1.2 Spectral and Weyl functions: inverse problem; 2.2 Weyl theory for Dirac system with a rectangularmatrix potential; 2.2.1 Direct problem; 2.2.2 Direct and inverse problems: explicit solutions; 2.3 Recovery of the Dirac system: general case; 2.3.1 Representation of the fundamental solution; 2.3.2 Weyl function: high energy asymptotics; 2.3.3 Inverse problem and Borg-Marchenko-type uniqueness theorem 2.3.4 Weyl function and positivity of S3 Skew-self-adjoint Dirac system: rectangular matrix potentials; 3.1 Direct problem; 3.2 The inverse problem on a finite interval and semiaxis; 3.3 System with a locally bounded potential; 4 Linear system auxiliary to the nonlinear optics equation; 4.1 Direct and inverse problems; 4.1.1 Bounded potentials; 4.1.2 Locally bounded potentials; 4.1.3 Weyl functions; 4.1.4 Some generalizations; 4.2 Conditions on the potential and asymptotics of generalized Weyl (GW) functions; 4.2.1 Preliminaries. Beals-Coifman asymptotics 4.2.2 Inverse problem and Borg-Marchenko-type result4.3 Direct and inverse problems: explicit solutions; 5 Discretesystems; 5.1 Discrete self-adjoint Dirac system; 5.1.1 Dirac system and Szegö recurrence; 5.1.2 Weyl theory: direct problems; 5.1.3 Weyl theory: inverse problems; 5.2 Discrete skew-self-adjoint Dirac system; 5.3 GBDT for the discrete skew-self-adjoint Dirac system; 5.3.1 Main results; 5.3.2 The fundamental solution; 5.3.3 Weyl functions: direct and inverse problems; 5.3.4 Isotropic Heisenberg magnet; 6 Integrable nonlinear equations 6.1 Compatibility condition and factorization formula6.1.1 Main results; 6.1.2 Proof of Theorem 6.1; 6.1.3 Application to the matrix "focusing" modified Korteweg-de Vries (mKdV); 6.1.4 Second harmonic generation: Goursat problem; 6.2 Sine-Gordon theory in a semistrip; 6.2.1 Complex sine-Gordon equation: evolution of the Weyl function and uniqueness of the solution; 6.2.2 Sine-Gordon equation in a semistrip; 6.2.3 Unbounded solutions in the quarter-plane; 7 General GBDT theorems and explicit solutions of nonlinear equations; 7.1 Explicit solutions of the nonlinear optics equation This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich. The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field |
| ctrlnum | (OCoLC)858762131 (DE-599)BVBBV043037065 |
| dewey-full | 515.357 515/.357 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.357 515/.357 |
| dewey-search | 515.357 515/.357 |
| dewey-sort | 3515.357 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043037065 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:39Z |
| institution | BVB |
| isbn | 3110258617 9783110258615 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028461713 |
| oclc_num | 858762131 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (356 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter studies in mathematics |
| spelling | Sakhnovich, Lev A. Verfasser aut Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions Berlin De Gruyter 2013 1 online resource (356 pages) txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics 7.2 GBDT for linear system depending rationally on z Print version record Preface; Notation; 0 Introduction; 1 Preliminaries; 1.1 Simple transformations and examples; 1.1.1 Dirac-type systems as a subclass of canonical systems; 1.1.2 Schrödinger systems as a subclass of canonical systems; 1.1.3 Gauge transformations of the Dirac systems; 1.2 S-nodes and Weyl functions; 1.2.1 Elementary properties of S-nodes; 1.2.2 Continual factorization; 1.2.3 Canonical systems and representation of the S-nodes; 1.2.4 Asymptotics of the Weyl functions, a special case; 1.2.5 Factorization of the operators S; 1.2.6 Weyl functions of Dirac and Schrödinger systems 2 Self-adjoint Dirac system: rectangular matrix potentials2.1 Square matrix potentials: spectral and Weyl theories; 2.1.1 Spectral and Weyl functions: direct problem; 2.1.2 Spectral and Weyl functions: inverse problem; 2.2 Weyl theory for Dirac system with a rectangularmatrix potential; 2.2.1 Direct problem; 2.2.2 Direct and inverse problems: explicit solutions; 2.3 Recovery of the Dirac system: general case; 2.3.1 Representation of the fundamental solution; 2.3.2 Weyl function: high energy asymptotics; 2.3.3 Inverse problem and Borg-Marchenko-type uniqueness theorem 2.3.4 Weyl function and positivity of S3 Skew-self-adjoint Dirac system: rectangular matrix potentials; 3.1 Direct problem; 3.2 The inverse problem on a finite interval and semiaxis; 3.3 System with a locally bounded potential; 4 Linear system auxiliary to the nonlinear optics equation; 4.1 Direct and inverse problems; 4.1.1 Bounded potentials; 4.1.2 Locally bounded potentials; 4.1.3 Weyl functions; 4.1.4 Some generalizations; 4.2 Conditions on the potential and asymptotics of generalized Weyl (GW) functions; 4.2.1 Preliminaries. Beals-Coifman asymptotics 4.2.2 Inverse problem and Borg-Marchenko-type result4.3 Direct and inverse problems: explicit solutions; 5 Discretesystems; 5.1 Discrete self-adjoint Dirac system; 5.1.1 Dirac system and Szegö recurrence; 5.1.2 Weyl theory: direct problems; 5.1.3 Weyl theory: inverse problems; 5.2 Discrete skew-self-adjoint Dirac system; 5.3 GBDT for the discrete skew-self-adjoint Dirac system; 5.3.1 Main results; 5.3.2 The fundamental solution; 5.3.3 Weyl functions: direct and inverse problems; 5.3.4 Isotropic Heisenberg magnet; 6 Integrable nonlinear equations 6.1 Compatibility condition and factorization formula6.1.1 Main results; 6.1.2 Proof of Theorem 6.1; 6.1.3 Application to the matrix "focusing" modified Korteweg-de Vries (mKdV); 6.1.4 Second harmonic generation: Goursat problem; 6.2 Sine-Gordon theory in a semistrip; 6.2.1 Complex sine-Gordon equation: evolution of the Weyl function and uniqueness of the solution; 6.2.2 Sine-Gordon equation in a semistrip; 6.2.3 Unbounded solutions in the quarter-plane; 7 General GBDT theorems and explicit solutions of nonlinear equations; 7.1 Explicit solutions of the nonlinear optics equation This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich. The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Boundary value problems fast Darboux transformations fast Evolution equations, Nonlinear fast Functions fast Inverse problems (Differential equations) fast Matrices fast Inverse problems (Differential equations) Evolution equations, Nonlinear Darboux transformations Boundary value problems Matrices Functions Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Darboux-Transformation (DE-588)4273823-4 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Inverses Problem (DE-588)4125161-1 s Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s Randwertproblem (DE-588)4048395-2 s Darboux-Transformation (DE-588)4273823-4 s 1\p DE-604 Sakhnovich, Alexander L. Sonstige oth Roitberg, Inna Ya Sonstige oth Erscheint auch als Druck-Ausgabe Sakhnovich, Lev A . Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl-Titchmarsh Functions http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=641731 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sakhnovich, Lev A. Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions Preface; Notation; 0 Introduction; 1 Preliminaries; 1.1 Simple transformations and examples; 1.1.1 Dirac-type systems as a subclass of canonical systems; 1.1.2 Schrödinger systems as a subclass of canonical systems; 1.1.3 Gauge transformations of the Dirac systems; 1.2 S-nodes and Weyl functions; 1.2.1 Elementary properties of S-nodes; 1.2.2 Continual factorization; 1.2.3 Canonical systems and representation of the S-nodes; 1.2.4 Asymptotics of the Weyl functions, a special case; 1.2.5 Factorization of the operators S; 1.2.6 Weyl functions of Dirac and Schrödinger systems 2 Self-adjoint Dirac system: rectangular matrix potentials2.1 Square matrix potentials: spectral and Weyl theories; 2.1.1 Spectral and Weyl functions: direct problem; 2.1.2 Spectral and Weyl functions: inverse problem; 2.2 Weyl theory for Dirac system with a rectangularmatrix potential; 2.2.1 Direct problem; 2.2.2 Direct and inverse problems: explicit solutions; 2.3 Recovery of the Dirac system: general case; 2.3.1 Representation of the fundamental solution; 2.3.2 Weyl function: high energy asymptotics; 2.3.3 Inverse problem and Borg-Marchenko-type uniqueness theorem 2.3.4 Weyl function and positivity of S3 Skew-self-adjoint Dirac system: rectangular matrix potentials; 3.1 Direct problem; 3.2 The inverse problem on a finite interval and semiaxis; 3.3 System with a locally bounded potential; 4 Linear system auxiliary to the nonlinear optics equation; 4.1 Direct and inverse problems; 4.1.1 Bounded potentials; 4.1.2 Locally bounded potentials; 4.1.3 Weyl functions; 4.1.4 Some generalizations; 4.2 Conditions on the potential and asymptotics of generalized Weyl (GW) functions; 4.2.1 Preliminaries. Beals-Coifman asymptotics 4.2.2 Inverse problem and Borg-Marchenko-type result4.3 Direct and inverse problems: explicit solutions; 5 Discretesystems; 5.1 Discrete self-adjoint Dirac system; 5.1.1 Dirac system and Szegö recurrence; 5.1.2 Weyl theory: direct problems; 5.1.3 Weyl theory: inverse problems; 5.2 Discrete skew-self-adjoint Dirac system; 5.3 GBDT for the discrete skew-self-adjoint Dirac system; 5.3.1 Main results; 5.3.2 The fundamental solution; 5.3.3 Weyl functions: direct and inverse problems; 5.3.4 Isotropic Heisenberg magnet; 6 Integrable nonlinear equations 6.1 Compatibility condition and factorization formula6.1.1 Main results; 6.1.2 Proof of Theorem 6.1; 6.1.3 Application to the matrix "focusing" modified Korteweg-de Vries (mKdV); 6.1.4 Second harmonic generation: Goursat problem; 6.2 Sine-Gordon theory in a semistrip; 6.2.1 Complex sine-Gordon equation: evolution of the Weyl function and uniqueness of the solution; 6.2.2 Sine-Gordon equation in a semistrip; 6.2.3 Unbounded solutions in the quarter-plane; 7 General GBDT theorems and explicit solutions of nonlinear equations; 7.1 Explicit solutions of the nonlinear optics equation This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich. The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Boundary value problems fast Darboux transformations fast Evolution equations, Nonlinear fast Functions fast Inverse problems (Differential equations) fast Matrices fast Inverse problems (Differential equations) Evolution equations, Nonlinear Darboux transformations Boundary value problems Matrices Functions Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Darboux-Transformation (DE-588)4273823-4 gnd Randwertproblem (DE-588)4048395-2 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4221363-0 (DE-588)4273823-4 (DE-588)4048395-2 (DE-588)4125161-1 |
| title | Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| title_auth | Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| title_exact_search | Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| title_full | Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| title_fullStr | Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| title_full_unstemmed | Inverse Problems and Nonlinear Evolution Equations Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| title_short | Inverse Problems and Nonlinear Evolution Equations |
| title_sort | inverse problems and nonlinear evolution equations solutions darboux matrices and weyl titchmarsh functions |
| title_sub | Solutions, Darboux Matrices and Weyl-Titchmarsh Functions |
| topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Boundary value problems fast Darboux transformations fast Evolution equations, Nonlinear fast Functions fast Inverse problems (Differential equations) fast Matrices fast Inverse problems (Differential equations) Evolution equations, Nonlinear Darboux transformations Boundary value problems Matrices Functions Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Darboux-Transformation (DE-588)4273823-4 gnd Randwertproblem (DE-588)4048395-2 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Boundary value problems Darboux transformations Evolution equations, Nonlinear Functions Inverse problems (Differential equations) Matrices Nichtlineare Evolutionsgleichung Darboux-Transformation Randwertproblem Inverses Problem |
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