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Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl-Titchmarsh Functions.
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 func...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
2013.
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| Colección: | De Gruyter studies in mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 049 | |a UAMI | ||
| 100 | 1 | |a Sakhnovich, Lev A. | |
| 245 | 1 | 0 | |a Inverse Problems and Nonlinear Evolution Equations : |b Solutions, Darboux Matrices and Weyl-Titchmarsh Functions. |
| 260 | |a Berlin : |b De Gruyter, |c 2013. | ||
| 300 | |a 1 online resource (356 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Studies in Mathematics | |
| 505 | 0 | |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. | |
| 500 | |a 7.2 GBDT for linear system depending rationally on z. | ||
| 520 | |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. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Inverse problems (Differential equations) | |
| 650 | 0 | |a Evolution equations, Nonlinear. | |
| 650 | 0 | |a Darboux transformations. | |
| 650 | 0 | |a Boundary value problems. | |
| 650 | 0 | |a Matrices. | |
| 650 | 0 | |a Functions. | |
| 650 | 6 | |a Problèmes inverses (Équations différentielles) | |
| 650 | 6 | |a Équations d'évolution non linéaires. | |
| 650 | 6 | |a Transformations de Darboux. | |
| 650 | 6 | |a Problèmes aux limites. | |
| 650 | 6 | |a Matrices. | |
| 650 | 6 | |a Fonctions (Mathématiques) | |
| 650 | 7 | |a functions (mathematics) |2 aat | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x 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 | 7 | |a Darboux-Transformation |2 gnd | |
| 650 | 7 | |a Nichtlineare Evolutionsgleichung |2 gnd | |
| 650 | 7 | |a Inverses Problem |2 gnd | |
| 650 | 7 | |a Randwertproblem |2 gnd | |
| 653 | |a Application. | ||
| 653 | |a Differential Equation. | ||
| 653 | |a Direct Problem. | ||
| 653 | |a Explicit Solution. | ||
| 653 | |a Global Solution. | ||
| 653 | |a Initial-Boundary-Value Problem. | ||
| 653 | |a Integrable Nonlinear Equation. | ||
| 653 | |a Inverse Problem. | ||
| 700 | 1 | |a Sakhnovich, Alexander L. | |
| 700 | 1 | |a Roitberg, Inna Ya. | |
| 776 | 0 | 8 | |i Print version: |a Sakhnovich, Lev A. |t Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl-Titchmarsh Functions. |d Berlin : De Gruyter, ©2013 |z 9783110258608 |
| 830 | 0 | |a De Gruyter studies in mathematics. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=641731 |z Texto completo |
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| 938 | |a De Gruyter |b DEGR |n 9783110258615 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL1121584 | ||
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