Inverse scattering on the line for a Dirac system
- 1 November 1991
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 32 (11) , 3015-3030
- https://doi.org/10.1063/1.529046
Abstract
The whole-line version of the Gelfand–Levitan–Marchenko (GLM) equation for a Dirac system is studied. A new derivation of the GLM equation is given, under weaker hypotheses than Frolov’s earlier treatment [Sov. Math. Dokl. 13, 1468 (1972)], and the complete inversion is carried out in some explicit cases in which a spectral gap is present. Previous calculations of this type are restricted either to a scalar potential or degenerate gap. Applications are discussed in connection with optical couplers and soliton equations.Keywords
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