LEADER 04547nam 22006375 450 001 9910483558203321 005 20200705223938.0 010 $a3-030-38431-4 024 7 $a10.1007/978-3-030-38431-9 035 $a(CKB)4100000011254666 035 $a(MiAaPQ)EBC6202753 035 $a(DE-He213)978-3-030-38431-9 035 $a(PPN)24839505X 035 $a(EXLCZ)994100000011254666 100 $a20200519d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDirect and Inverse Scattering for the Matrix Schrödinger Equation$b[electronic resource] /$fby Tuncay Aktosun, Ricardo Weder 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (xiii, 624 pages) 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v203 311 $a3-030-38430-6 320 $aIncludes bibliographical references and index. 327 $aThe matrix Schrödinger equation and the characterization of the scattering data -- Direct scattering I -- Direct scattering II -- Inverse scattering -- Some explicit examples -- Mathematical preliminaries. 330 $aAuthored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set. 410 0$aApplied Mathematical Sciences,$x0066-5452 ;$v203 606 $aPartial differential equations 606 $aFunctional analysis 606 $aQuantum physics 606 $aMathematical physics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aPartial differential equations. 615 0$aFunctional analysis. 615 0$aQuantum physics. 615 0$aMathematical physics. 615 14$aPartial Differential Equations. 615 24$aFunctional Analysis. 615 24$aQuantum Physics. 615 24$aMathematical Physics. 676 $a515.724 700 $aAktosun$b Tuncay$4aut$4http://id.loc.gov/vocabulary/relators/aut$01221266 702 $aWeder$b Ricardo$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483558203321 996 $aDirect and Inverse Scattering for the Matrix Schrödinger Equation$92831969 997 $aUNINA