Small-energy asymptotics of the scattering matrix for the matrix Schrödinger equation on the line

DOI10.1063/1.1398059zbMath1017.81046OpenAlexW2077169358MaRDI QIDQ2774676

Tuncay Aktosun, Cornelis V. M. van der Mee, Martin Klaus

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10919/25113

zbMATH Keywords

scattering coefficientsfinite first momentssmall-energy asymptoticsintegrable matrix entries

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) (S)-matrix theory, etc. in quantum theory (81U20) Inverse problems involving ordinary differential equations (34A55) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (15)

A matrix Schrödinger approach to focusing nonlinear Schrödinger equations with nonvanishing boundary conditions ⋮ On bound states for systems of weakly coupled Schrödinger equations in one space dimension ⋮ Determination of the self-adjoint matrix Schrödinger operators without the bound state data ⋮ Stability of the inverse scattering problem for the self‐adjoint matrix Schrödinger operator on the half line ⋮ From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems ⋮ Factorization for the Full-Line Matrix Schrödinger Equation and a Unitary Transformation to the Half-Line Scattering ⋮ The matrix nonlinear Schrödinger equation with a potential ⋮ Analyticity properties of the scattering matrix for matrix Schrödinger operators on the discrete line ⋮ A Wronskian of Jost solutions ⋮ Small-energy analysis for the selfadjoint matrix Schrödinger operator on the half line. II ⋮ On a fundamental system of solutions of the matrix Schrödinger equation with a polynomial energy-dependent potential ⋮ The \(L^p\) boundedness of the wave operators for matrix Schrödinger equations ⋮ Small-energy analysis for the self-adjoint matrix Schrödinger operator on the half line ⋮ Wave and scattering operators for the nonlinear matrix Schrödinger equation on the half-line with a potential ⋮ Band edge limit of the scattering matrix for quasi-one-dimensional discrete Schrödinger operators

Cites Work

• Inverse problem for Sturm-Liouville operators with rational reflection coefficient
• On the Extension of Inverse Scattering Method
• Spectral properties of Schrodinger operators with matrix potentials. II
• Low-energy behaviour of the scattering matrix for the Schrodinger equation on the line
• Inverse scattering on the line
• Inverse scattering transform for general matrix Schrodinger operators and the related symplectic structure
• Trace identities in the inverse scattering transform method associated with matrix Schrödinger operators

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