Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté. Image fixe : sans médiation
Auteur(s) : Sakhnovich, Alexander L.
Sakhnovich, L. A.
Roitberg, Inna Ya.
Titre(s) : Inverse problems and nonlinear evolution equations [Texte imprimé] : solutions, Darboux matrices and Weyl-Titchmarsh functions / Alexander L. Sakhnovich, Lev A. Sakhnovich, Inna Ya. Roitberg
Publication : Berlin : W. de Gruyter, 2013
Description matérielle : 1 vol. (XIII-341 p.) : ill. ; 25 cm
Collection : De Gruyter studies in mathematics ; 47
Lien à la collection : De Gruyter studies in mathematics
Comprend : Preface ; Notation ; Preliminaries ; Self-adjoint Dirac system : rectangular matrix
potentials - Skew-self-adjoint Dirac system : rectangular matrix potentials ; Linear
system auxiliary to the nonlinear optics equation ; Discrete systems ; Integrable
nonlinear equations ; General GBDT theorems and explicit solutions of nonlinear equations
; Some further results on inverse problems and generalized Bäcklund-Darboux transformation
(GBDT) ; 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.
Note(s) : Bibliogr.p. 323-338
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. -- Publisher website
Sujet(s) : Problèmes inverses (équations différentielles)
Équations d'évolution non linéaires
Darboux, Transformations de
Problèmes aux limites
Indice(s) Dewey :
515.357 (23e éd.) = Problèmes inverses
Identifiants, prix et caractéristiques : ISBN 9783110258608. - ISBN 3110258609 (rel.). - ISBN 9783110258615. - ISBN 3110258617
(ebk). - ISBN 9783112205006. - ISBN 3112205006 (set)
Identifiant de la notice : ark:/12148/cb43604125h
Notice n° :
FRBNF43604125
(notice reprise d'un réservoir extérieur)
