Inverse scattering transform for general matrix Schrodinger operators and the related symplectic structure
- 1 August 1985
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 1 (3) , 219-236
- https://doi.org/10.1088/0266-5611/1/3/007
Abstract
The general matrix Schrodinger problem is studied and the corresponding equations for the inverse scattering method are obtained. Appropriate modifications lead to a derivation of the generalised Gel'fand-Levitan-Marchenko equations for the case in which there are double poles of the matrix A-1(k). The symplectic structure associated with the non-linear evolution equations of this formalism is also investigated. Special attention is paid to the derivation of the Poisson bracket of the reflection coefficients.Keywords
This publication has 12 references indexed in Scilit:
- A method of approximate calculation of Feynman diagrams. ITheoretical and Mathematical Physics, 1983
- Trace identities in the inverse scattering transform method associated with matrix Schrödinger operatorsJournal of Mathematical Physics, 1982
- Commutation relations of the transition matrix in the classical and quantum inverse scattering methods (local case)Theoretical and Mathematical Physics, 1981
- Infinite-dimensional Hamiltonian systems associated with matrix Schrödinger operatorsIl Nuovo Cimento B (1971-1996), 1981
- Inverse scattering on the lineCommunications on Pure and Applied Mathematics, 1979
- Nonlinear evolution equations solvable by the inverse spectral transform.— IIIl Nuovo Cimento B (1971-1996), 1977
- On the Extension of Inverse Scattering MethodProgress of Theoretical Physics, 1974
- Properties of the 𝑆-matrix of the one-dimensional Schrödinger equationAmerican Mathematical Society Translations: Series 2, 1967
- A Singular Boundary Value Problem for a Non-Self-Adjoint Differential OperatorCanadian Journal of Mathematics, 1958
- The construction of potentials from theS-matrix for systems of differential equationsIl Nuovo Cimento (1869-1876), 1955