Virginia TechHinton, D. B.Jordan, A. K.Klaus, MartinShaw, John Kenneth2014-01-232014-01-231991-11Hinton, DB; Jordan, AK; Klaus, M; et al., "Inverse scattering on the line for a Dirac system," J. Math. Phys. 32, 3015 (1991); http://dx.doi.org/10.1063/1.5290460022-2488http://hdl.handle.net/10919/25119The 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. Dok1. 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.en-USIn CopyrightArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/32/11/10.1063/1.529046https://doi.org/10.1063/1.529046