Inverse scattering on the line for a Dirac system
Hinton, D. B.
Jordan, A. K.
Shaw, J. K.
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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. 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.