LEADER 04878nam 2200781 450 001 9910462666203321 005 20211216205554.0 024 7 $a10.1515/9783110258615 035 $a(CKB)2670000000432708 035 $a(EBL)1121584 035 $a(OCoLC)858762131 035 $a(SSID)ssj0001002014 035 $a(PQKBManifestationID)11555150 035 $a(PQKBTitleCode)TC0001002014 035 $a(PQKBWorkID)10995751 035 $a(PQKB)10236007 035 $a(MiAaPQ)EBC1121584 035 $a(DE-B1597)124070 035 $a(OCoLC)856565338 035 $a(DE-B1597)9783110258615 035 $a(PPN)18293750X 035 $a(Au-PeEL)EBL1121584 035 $a(CaPaEBR)ebr10786169 035 $a(CaONFJC)MIL807731 035 $a(EXLCZ)992670000000432708 100 $a20131008h20132013 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aInverse problems and nonlinear evolution equations $esolutions, Darboux matrices and Weyl-Titchmarsh functions /$fby Alexander Sakhnovich, Lev Sakhnovich, Inna Roitberg 210 1$aBerlin ;$aBoston :$cWalter de Gruyter GmbH & Co., KG,$d[2013] 210 4$d©2013 215 $a1 online resource (356 p.) 225 0 $aDe Gruyter Studies in Mathematics ;$v47 300 $aDescription based upon print version of record. 311 0 $a3-11-025861-7 311 0 $a3-11-025860-9 320 $aIncludes bibliographies and index. 327 $tFront matter --$tPreface --$tNotation --$tContents --$t0 Introduction --$t1 Preliminaries --$t2 Self-adjoint Dirac system: rectangular matrix potentials --$t3 Skew-self-adjoint Dirac system: rectangular matrix potentials --$t4 Linear system auxiliary to the nonlinear optics equation --$t5 Discrete systems --$t6 Integrable nonlinear equations --$t7 General GBDT theorems and explicit solutions of nonlinear equations --$t8 Some further results on inverse problems and generalized Bäcklund-Darboux transformation (GBDT) --$t9 Sliding inverse problems for radial Dirac and Schrödinger equations --$tAppendices --$tA General-type canonical system: pseudospectral and Weyl functions --$tB Mathematical system theory --$tC Krein's system --$tD Operator identities corresponding to inverse problems --$tE Some basic theorems --$tBibliography --$tIndex 330 $aThis book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund-Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses. 410 3$aDe Gruyter Studies in Mathematics 606 $aBoundary value problems 606 $aDarboux transformations 606 $aEvolution equations, Nonlinear 606 $aFunctions 606 $aInverse problems (Differential equations) 606 $aMatrices 608 $aElectronic books. 615 0$aBoundary value problems. 615 0$aDarboux transformations. 615 0$aEvolution equations, Nonlinear. 615 0$aFunctions. 615 0$aInverse problems (Differential equations) 615 0$aMatrices. 676 $a515.357 676 $a515/.357 700 $aSakhnovich$b Alexander$0740259 701 $aRoitberg$b Inna$01035590 701 $aSakhnovich$b L. A$0348825 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462666203321 996 $aInverse problems and nonlinear evolution equations$92455363 997 $aUNINA